Phase synchronization of chaotic oscillators

A novel method linking neural connectivity to behavioral fluctuations: Behavior-regressed connectivity

BACKGROUND

During an experimental session, behavioral performance fluctuates, yet most neuroimaging analyses of functional connectivity derive a single connectivity pattern. These conventional connectivity approaches assume that since the underlying behavior of the task remains constant, the connectivity pattern is also constant.

NEW METHOD

We introduce a novel method, behavior-regressed connectivity (BRC), to directly examine behavioral fluctuations within an experimental session and capture their relationship to changes in functional connectivity. This method employs the weighted phase lag index (WPLI) applied to a window of trials with a weighting function. Using two datasets, the BRC results are compared to conventional connectivity results during two time windows: the one second before stimulus onset to identify predictive relationships, and the one second after onset to capture task-dependent relationships.

RESULTS

In both tasks, we replicate the expected results for the conventional connectivity analysis, and extend our understanding of the brain-behavior relationship using the BRC analysis, demonstrating subject-specific BRC maps that correspond to both positive and negative relationships with behavior. Comparison with Existing Method(s): Conventional connectivity analyses assume a consistent relationship between behaviors and functional connectivity, but the BRC method examines performance variability within an experimental session to understand dynamic connectivity and transient behavior.

CONCLUSION

The BRC approach examines connectivity as it covaries with behavior to complement the knowledge of underlying neural activity derived from conventional connectivity analyses. Within this framework, BRC may be implemented for the purpose of understanding performance variability both within and between participants.

Disrupted global metastability and static and dynamic brain connectivity across individuals in the Alzheimer's disease continuum

As findings on the neuropathological and behavioral components of Alzheimer's disease (AD) continue to accrue, converging evidence suggests that macroscale brain functional disruptions may mediate their association. Recent developments on theoretical neuroscience indicate that instantaneous patterns of brain connectivity and metastability may be a key mechanism in neural communication underlying cognitive performance. However, the potential significance of these patterns across the AD spectrum remains virtually unexplored. We assessed the clinical sensitivity of static and dynamic functional brain disruptions across the AD spectrum using resting-state fMRI in a sample consisting of AD patients (n = 80) and subjects with either mild (n = 44) or subjective (n = 26) cognitive impairment (MCI, SCI). Spatial maps constituting the nodes in the functional brain network and their associated time-series were estimated using spatial group independent component analysis and dual regression, and whole-brain oscillatory activity was analyzed both globally (metastability) and locally (static and dynamic connectivity). Instantaneous phase metrics showed functional coupling alterations in AD compared to MCI and SCI, both static (putamen, dorsal and default-mode) and dynamic (temporal, frontal-superior and default-mode), along with decreased global metastability. The results suggest that brains of AD patients display altered oscillatory patterns, in agreement with theoretical premises on cognitive dynamics.

Direct coupling: a possible strategy to control fruit production in alternate bearing

We investigated the theoretical possibility of applying phenomenon of synchronization of coupled nonlinear oscillators to control alternate bearing in citrus. The alternate bearing of fruit crops is a phenomenon in which a year of heavy yield is followed by an extremely light one. This phenomenon has been modeled previously by the resource budget model, which describes a typical nonlinear oscillator of the tent map type. We have demonstrated how direct coupling, which could be practically realized through grafting, contributes to the nonlinear dynamics of alternate bearing, especially phase synchronization. Our results show enhancement of out-of-phase synchronization in production, which depends on initial conditions obtained under the given system parameters. Based on these numerical experiments, we propose a new method to control alternate bearing, say in citrus, thereby enabling stable fruit production. The feasibility of validating the current results through field experimentation is also discussed.

Mechanical ventilatory modes and cardioventilatory phase synchronization in acute respiratory failure patients

Cardioventilatory phase synchronization was studied in ten critically ill patients admitted in intensive care unit (ICU) for acute respiratory failure under two mechanical ventilatory modes: (i) pressure controlled ventilation (PCV); (ii) pressure support ventilation (PSV). The two modalities were administered to the same patient in different times in a random order. Cardioventilatory phase interactions were typified by plotting the relative position of a heartbeat, detected from the electrocardiogram and collected in n groups, within m ventilatory cycles as a function of the progressive cardiac beat number via the synchrogram. n:m phase synchronized patterns were detected by computing the variability of each phase group. The percent duration of the recording featuring phase synchronization was assessed as a measure of the strength of phase synchrony and tested against situations of full phase desynchronization between cardiac and ventilatory rhythms. Indexes quantifying the variability of the cardiac and ventilatory activities were computed as well. Findings proved that: (i) a significant presence of n:m phase synchronized patterns was detected in PCV; (ii) the strength of n:m phase synchronization was stronger during PCV than PSV; (iii) different strengths of cardioventilatory phase synchronization detected during PCV and PSV were found in presence of similar heart and ventilatory rates and alike variability. We conclude that mechanical ventilation can induce a significant presence of cardioventilatory phase synchronized patterns and this amount depends on the mode of mechanical ventilation. Future studies should test the eventual link of the level of phase coordination between heart and mechanical ventilation to a clinical outcome to understand whether featuring a certain degree of cardioventilatory phase synchronization is beneficial for the critical patient in ICU.

Optimal phase synchronization in networks of phase-coherent chaotic oscillators

We investigate the existence of an optimal interplay between the natural frequencies of a group of chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase synchronization in the most effective way, i.e., with the lowest possible coupling strength. Specifically, we show by means of numerical and experimental results that it is possible to define a synchrony alignment function J(ω,L) linking the natural frequencies ω_i of a set of non-identical phase-coherent chaotic oscillators with the topology of the Laplacian matrix L, the latter accounting for the specific organization of the network of interactions between oscillators. We use the classical Rössler system to show that the synchrony alignment function obtained for phase oscillators can be extended to phase-coherent chaotic systems. Finally, we carry out a series of experiments with nonlinear electronic circuits to show the robustness of the theoretical predictions despite the intrinsic noise and parameter mismatch of the electronic components.

Finite-time synchronization for recurrent neural networks with discontinuous activations and time-varying delays

In this paper, we study the finite-time synchronization problem for recurrent neural networks with discontinuous activations and time-varying delays. Based on the finite-time convergence theory and by using the nonsmooth analysis technique, some finite-time synchronization criteria for the considered neural network model are established, which are new and complement some existing ones. The feasibility and effectiveness of the proposed synchronization method are supported by two examples with numerical simulations.

High-order synchronization of hair cell bundles

Auditory and vestibular hair cell bundles exhibit active mechanical oscillations at natural frequencies that are typically lower than the detection range of the corresponding end organs. We explore how these noisy nonlinear oscillators mode-lock to frequencies higher than their internal clocks. A nanomagnetic technique is used to stimulate the bundles without an imposed mechanical load. The evoked response shows regimes of high-order mode-locking. Exploring a broad range of stimulus frequencies and intensities, we observe regions of high-order synchronization, analogous to Arnold Tongues in dynamical systems literature. Significant areas of overlap occur between synchronization regimes, with the bundle intermittently flickering between different winding numbers. We demonstrate how an ensemble of these noisy spontaneous oscillators could be entrained to efficiently detect signals significantly above the characteristic frequencies of the individual cells.

Detecting Mild Traumatic Brain Injury Using Resting State Magnetoencephalographic Connectivity

Accurate means to detect mild traumatic brain injury (mTBI) using objective and quantitative measures remain elusive. Conventional imaging typically detects no abnormalities despite post-concussive symptoms. In the present study, we recorded resting state magnetoencephalograms (MEG) from adults with mTBI and controls. Atlas-guided reconstruction of resting state activity was performed for 90 cortical and subcortical regions, and calculation of inter-regional oscillatory phase synchrony at various frequencies was performed. We demonstrate that mTBI is associated with reduced network connectivity in the delta and gamma frequency range (>30 Hz), together with increased connectivity in the slower alpha band (8–12 Hz). A similar temporal pattern was associated with correlations between network connectivity and the length of time between the injury and the MEG scan. Using such resting state MEG network synchrony we were able to detect mTBI with 88% accuracy. Classification confidence was also correlated with clinical symptom severity scores. These results provide the first evidence that imaging of MEG network connectivity, in combination with machine learning, has the potential to accurately detect and determine the severity of mTBI.

Detecting concussion is typically not possible using currently clinically used brain imaging, such as MRI and CT scans. Magnetoencephalographic (MEG) imaging is able to directly measure brain activity at fast time scales, and this can be used to map how various areas of the brain interact. We recorded MEG from individuals who had suffered a concussion, as well as control subjects who had not. We found characteristic alterations of inter-regional interactions associated with concussion. Moreover, using a machine learning approach, we were able to detect concussion with 88% accuracy from MEG connectivity, and confidence of classification correlated with symptom severity. This potentially provides new quantitative and objective methods for detecting and assessing the severity of concussion using neuroimaging.

On the estimation of phase synchronization, spurious synchronization and filtering

Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M. Chavez et al., J. Neurosci. Methods 154, 149 (2006)]. If this condition is not fulfilled, band-pass filtering seems to be the adequate technique in order to pre-process data for a posterior synchronization analysis. However, it was reported that band-pass filtering might induce spurious synchronization [L. Xu et al., Phys. Rev. E 73, 065201(R), (2006); J. Sun et al., Phys. Rev. E 77, 046213 (2008); and J. Wang and Z. Liu, EPL 102, 10003 (2013)], a statement that without further specification causes uncertainty over all measures that aim to quantify phase synchronization of broadband field data. We show by using signals derived from different test frameworks that appropriate filtering does not induce spurious synchronization. Instead, filtering in the time domain tends to wash out existent phase interrelations between signals. Furthermore, we show that measures derived for the estimation of phase synchronization like the mean phase coherence are also useful for the detection of interrelations between time series, which are not necessarily derived from coupled self-sustained nonlinear oscillators.

Time-frequency phase-synchrony approaches with ERPs

Time-frequency signal processing approaches are well-developed, and have been widely employed for the study of the energy distribution of event-related potential (ERP) data across time and frequency. Wavelet time-frequency transform (TFT) and Cohen's class of time-frequency distributions (TFD) are the most widely used in the field. While ERP TFT approaches have been most extensively developed for amplitude measures, reflecting the magnitude of regional neuronal activity, time-frequency phase-synchrony measures have gained increased utility in recent years for the assessment of functional connectivity. Phase synchrony measures can be used to index the functional integration between regions (interregional), in addition to the consistency of activity within region (intertrial). In this paper, we focus on a particular class of time-frequency distributions belonging to Cohen's class, known as the Reduced Interference Distribution (RID) for quantifying functional connectivity, which we recently introduced (Aviyente et al., 2011). The present report first summarizes common time-frequency approaches to computing phase-synchrony with ERP data in order to highlight the similarities and differences relative to the RID. In previous work, we demonstrated differences between the RID and wavelet approaches to indexing phase-synchrony, and have applied the RID to demonstrate that RID-based time-frequency phase-synchrony measures can index increased functional connectivity between medial and lateral prefrontal regions during control processing, observed in the theta band during the error-related negativity (ERN). Because ERN amplitude measures have been associated with two other widely studied medial-frontal theta components (no-go N2; feedback negativity, FN), the application of the RID phase synchrony measure in the present report extends our previous work with ERN to include theta activity during the no-go N2 (inhibitory processing) and the feedback negativity (FN; loss feedback processing). Findings support the idea that similar medial-lateral prefrontal functional connectivity underlies the ERN, no-go N2, and FN components, and provide initial validation that the proposed RID-based time-frequency phase-synchrony measure can index this activity.

Heteroclinic dynamics of coupled semiconductor lasers with optoelectronic feedback

Generalized Lotka-Volterra (GLV) equations are important equations used in various areas of science to describe competitive dynamics among a population of N interacting nodes in a network topology. In this Letter, we introduce a photonic network consisting of three optoelectronically cross-coupled semiconductor lasers to realize a GLV model. In such a network, the interaction of intensity and carrier inversion rates, as well as phases of laser oscillator nodes, result in various dynamics. We study the influence of asymmetric coupling strength and frequency detuning between semiconductor lasers and show that inhibitory asymmetric coupling is required to achieve consecutive amplitude oscillations of the laser nodes. These studies were motivated primarily by the dynamical models used to model brain cognitive activities and their correspondence with dynamics obtained among coupled laser oscillators.

Influences on and Measures of Unintentional Group Synchrony

Many instances of large-scale coordination occur in real-life social situations without the explicit awareness of the individuals involved. While the majority of research to date has examined dyadic interactions – those between two individuals – during intentional or deliberate coordination, the present review surveys the handful of recent studies investigating behavioral and physiological synchrony across groups of more than two people when coordination was not an explicit goal. Both minimal (e.g., visual information, shared location) and naturalistic (e.g., choir voice section, family relationship) group interactions appear to promote unintentional group synchrony although they have so far only been studied separately. State differences in unintentional group synchrony, or the relative presence of coordination in various conditions, have tended to be assessed differently, such as using correlation-type relationships, compared to its temporal dynamics, or changes over time in the degree of coordination, which appear to be best captured using phase differences. Simultaneously evaluating behavioral, physiological, and social responses as well systematically comparing different synchrony measures could further our understanding of the influences on and measures of group synchrony, allowing us to move away from studying individual persons responding to static laboratory stimuli and toward investigating collective experiences in natural, dynamic social interactions.

Function projective synchronization of complex networks with asymmetric coupling via adaptive and pinning feedback control

The problem on function projective synchronization (FPS) is investigated for complex networks via hybrid control. In contrast to existing works, the asymmetric coupling matrix was considered. Based on adaptive and pinning feedback control methods, new FPS criteria are proposed. Finally, three examples are provided to illustrate the effectiveness of the proposed methods.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

Traveling phase waves in asymmetric networks of noisy chaotic attractors

We explore identical Rössler systems organized into two equally sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. With this asymmetric coupling, we analyze patterns in the phase dynamics that coexist with chaotic amplitudes. We specifically investigate traveling phase waves where the oscillators settle on a new rhythm different from their own. We show that these waves are possible even without coherence in the phase angles. It is further demonstrated that the emergence of these incoherent traveling waves depends on the type of coupling, not on the individual dynamics of the Rössler systems. Together with the study of noise effects, our results suggest a promising new avenue toward the interplay of chaotic, noisy, coherent, and incoherent collective dynamics.

Detection and counting of a submicrometer particle in liquid flow by self-mixing microchip Yb:YAG laser velocimetry

We observed intermittent modulation by scattered light from a single submicrometer particle moving in the flow channel using a self-mixing microchip Yb:YAG laser Doppler velocimeter (LDV) under lateral beam access. The Doppler-shift frequency chirping (i.e., velocity change) was identified in accordance with a particle passage through the beam focus. Single particle counting, which obeys the Poisson distribution, was performed successfully over a long period of time. The experimental results have been reproduced by a numerical simulation. The LDV signal was increased over 20 dB for a 202-nm particle without chirping by collinear beam access with the laser beam axis aligned along the flow direction.

Synchronizing noisy nonidentical oscillators by transient uncoupling

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them-a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.

Reviving oscillation with optimal spatial period of frequency distribution in coupled oscillators

The spatial distributions of system's frequencies have significant influences on the critical coupling strengths for amplitude death (AD) in coupled oscillators. We find that the left and right critical coupling strengths for AD have quite different relations to the increasing spatial period m of the frequency distribution in coupled oscillators. The left one has a negative linear relationship with m in log-log axis for small initial frequency mismatches while remains constant for large initial frequency mismatches. The right one is in quadratic function relation with spatial period m of the frequency distribution in log-log axis. There is an optimal spatial period m₀ of frequency distribution with which the coupled system has a minimal critical strength to transit from an AD regime to reviving oscillation. Moreover, the optimal spatial period m₀ of the frequency distribution is found to be related to the system size N. Numerical examples are explored to reveal the inner regimes of effects of the spatial frequency distribution on AD.

Experimental evidence of deterministic coherence resonance in coupled chaotic systems with frequency mismatch

We present the experimental evidence of deterministic coherence resonance in unidirectionally coupled two and three Rössler electronic oscillators with mismatch between their natural frequencies. The regularity in both the amplitude and the phase of chaotic fluctuations is experimentally proven by the analyses of normalized standard deviations of the peak amplitude and interpeak interval and Lyapunov exponents. The resonant chaos suppression appears when the coupling strength is increased and the oscillators are in phase synchronization. In two coupled oscillators, the coherence enhancement is associated with negative third and fourth Lyapunov exponents, while the largest first and second exponents remain positive. Distinctly, in three oscillators coupled in a ring, all exponents become negative, giving rise to periodicity. Numerical simulations are in good agreement with the experiments.

Migraine — New Perspectives from Chaos Theory

Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms.

Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins

We study the multistability that results when a chaotic response system that has an invariant symmetry is driven by another chaotic oscillator. We observe that there is a transition from a desynchronized state to a situation of multistability. In the case considered, there are three coexisting attractors, two of which are synchronized and one is desynchronized. For large coupling, the asynchronous attractor disappears, leaving the system bistable. We study the basins of attraction of the system in the regime of multistability. The three attractor basins are interwoven in a complex manner, with extensive riddling within a sizeable region of (but not the entire) phase space. A quantitative characterization of the riddling behavior is made via the so-called uncertainty exponent, as well as by evaluating the scaling behavior of tongue-like structures emanating from the synchronization manifold.

Bispectral pairwise interacting source analysis for identifying systems of cross-frequency interacting brain sources from electroencephalographic or magnetoencephalographic signals

Brain cognitive functions arise through the coordinated activity of several brain regions, which actually form complex dynamical systems operating at multiple frequencies. These systems often consist of interacting subsystems, whose characterization is of importance for a complete understanding of the brain interaction processes. To address this issue, we present a technique, namely the bispectral pairwise interacting source analysis (biPISA), for analyzing systems of cross-frequency interacting brain sources when multichannel electroencephalographic (EEG) or magnetoencephalographic (MEG) data are available. Specifically, the biPISA makes it possible to identify one or many subsystems of cross-frequency interacting sources by decomposing the antisymmetric components of the cross-bispectra between EEG or MEG signals, based on the assumption that interactions are pairwise. Thanks to the properties of the antisymmetric components of the cross-bispectra, biPISA is also robust to spurious interactions arising from mixing artifacts, i.e., volume conduction or field spread, which always affect EEG or MEG functional connectivity estimates. This method is an extension of the pairwise interacting source analysis (PISA), which was originally introduced for investigating interactions at the same frequency, to the study of cross-frequency interactions. The effectiveness of this approach is demonstrated in simulations for up to three interacting source pairs and for real MEG recordings of spontaneous brain activity. Simulations show that the performances of biPISA in estimating the phase difference between the interacting sources are affected by the increasing level of noise rather than by the number of the interacting subsystems. The analysis of real MEG data reveals an interaction between two pairs of sources of central mu and beta rhythms, localizing in the proximity of the left and right central sulci.

Unbiased and robust quantification of synchronization between spikes and local field potential

BACKGROUND

In neuroscience, relating the spiking activity of individual neurons to the local field potential (LFP) of neural ensembles is an increasingly useful approach for studying rhythmic neuronal synchronization. Many methods have been proposed to measure the strength of the association between spikes and rhythms in the LFP recordings, and most existing measures are dependent upon the total number of spikes.

NEW METHOD

In the present work, we introduce a robust approach for quantifying spike-LFP synchronization which performs reliably for limited samples of data. The measure is termed as spike-triggered correlation matrix synchronization (SCMS), which takes LFP segments centered on each spike as multi-channel signals and calculates the index of spike-LFP synchronization by constructing a correlation matrix.

RESULTS

The simulation based on artificial data shows that the SCMS output almost does not change with the sample size. This property is of crucial importance when making comparisons between different experimental conditions. When applied to actual neuronal data recorded from the monkey primary visual cortex, it is found that the spike-LFP synchronization strength shows orientation selectivity to drifting gratings.

COMPARISON WITH EXISTING METHODS

In comparison to another unbiased method, pairwise phase consistency (PPC), the proposed SCMS behaves better for noisy spike trains by means of numerical simulations.

CONCLUSIONS

This study demonstrates the basic idea and calculating process of the SCMS method. Considering its unbiasedness and robustness, the measure is of great advantage to characterize the synchronization between spike trains and rhythms present in LFP.

Inhomogeneity induces relay synchronization in complex networks

Relay synchronization is a collective state, originally found in chains of interacting oscillators, in which uncoupled dynamical units synchronize through the action of mismatched inner nodes that relay the information but do not synchronize with them. It is demonstrated herein that relay synchronization is not limited to such simple motifs, rather it can emerge in larger and arbitrary network topologies. In particular, we show how this phenomenon can be observed in networks of chaotic systems in the presence of some mismatched units, the relay nodes, and how it is actually responsible for an enhancement of synchronization in the network.

On the dynamics of Liesegang-type pattern formation in a gaseous system

Liesegang pattern formations are widely spread in nature. In spite of a comparably simple experimental setup under laboratory conditions, a variety of spatio-temporal structures may arise. Presumably because of easier control of the experimental conditions, Liesegang pattern formation was mainly studied in gel systems during more than a century. Here we consider pattern formation in a gas phase, where beautiful but highly complex reaction-diffusion-convection dynamics are uncovered by means of a specific laser technique. A quantitative analysis reveals that two different, apparently independent processes, both highly correlated and synchronized across the extension of the reaction cloud, act on different time scales. Each of them imprints a different structure of salt precipitation at the tube walls.

Devil's staircase in an optomechanical cavity

We study self-excited oscillations (SEOs) in an on-fiber optomechanical cavity. While the phase of SEOs randomly diffuses in time when the laser power injected into the cavity is kept constant, phase locking may occur when the laser power is periodically modulated in time. We investigate the dependence of phase locking on the amplitude and frequency of the laser-power modulation. We find that phase locking can be induced with a relatively low modulation amplitude provided that the ratio between the modulation frequency and the frequency of SEOs is tuned close to a rational number of relatively low hierarchy in the Farey tree. To account for the experimental results, a one-dimensional map, which allows evaluating the time evolution of the phase of SEOs, is theoretically derived. By calculating the winding number of the one-dimensional map, the regions of phase locking can be mapped in the plane of modulation amplitude and modulation frequency. Comparison between the theoretical predictions and the experimental findings yields a partial agreement.

Optimal Extraction of Collective Oscillations from Unreliable Measurements

We present a method that facilitates a phase description of collective, irregular-oscillatory dynamics from unreliable multichannel recordings. The collective oscillations may be represented in each channel with fluctuating amplitude, phase offsets, and substantial amounts of measurement noise. Our method performs well under such realistic conditions, as we exemplify with collective brain rhythms in multichannel electroencephalogram recordings.

Seizure Prediction and Detection via Phase and Amplitude Lock Values

A robust seizure prediction methodology would enable a “closed-loop” system that would only activate as impending seizure activity is detected. Such a system would eliminate ongoing stimulation to the brain, thereby eliminating such side effects as coughing, hoarseness, voice alteration, and paresthesias (Murphy et al., 1998; Ben-Menachem, 2001), while preserving overall battery life of the system. The seizure prediction and detection algorithm uses Phase/Amplitude Lock Values (PLV/ALV) which calculate the difference of phase and amplitude between electroencephalogram (EEG) electrodes local and remote to the epileptic event. PLV is used as the seizure prediction marker and signifies the emergence of abnormal neuronal activations through local neuron populations. PLV/ALVs are used as seizure detection markers to demarcate the seizure event, or when the local seizure event has propagated throughout the brain turning into a grand-mal event. We verify the performance of this methodology against the “CHB-MIT Scalp EEG Database” which features seizure attributes for testing. Through this testing, we can demonstrate a high degree of sensivity and precision of our methodology between pre-ictal and ictal events.

Experimental synchrony of semiconductor lasers in coupled networks

The emission and synchronization of mutually-coupled semiconductor lasers with short cavities has been already recorded, with transversely unstable solutions existing within the chaotic synchronization manifold. Noise and laser-mismatch induced instabilities cause short de-synchronization events within the overall generalized synchronization, influencing the pragmatism of using these signals in secure data exchange applications. However, such operation can be functional for user authentication and sensing applications by assessing a time-averaged performance of synchrony. Until now, this has not been examined either in large-scale laser network configurations or in large transmission coupling paths, as real network implementations oblige. Here we present the first implementation of a fully-coupled fiber network with up to 16 semiconductor lasers, independently controlled and coupled through long interacting cavities. High level of consistent global or cluster synchrony via chaotic signals is demonstrated among all devices of the same origin and under appropriate operation. Devices that are not identical fail to synchronize at any condition, when coupled to the network. Under multiplexed operation, groups of lasers that emit at spectral distances as low as 50pm are shown to preserve intra-cluster synchronization when transmitted in the same fiber-optic channel, despite their large bandwidth of emitted signals.

Lag Synchronization of Memristor-Based Coupled Neural Networks via ω-Measure

This paper deals with the lag synchronization problem of memristor-based coupled neural networks with or without parameter mismatch using two different algorithms. Firstly, we consider the memristor-based neural networks with parameter mismatch, lag complete synchronization cannot be achieved due to parameter mismatch, the concept of lag quasi-synchronization is introduced. Based on the ω-measure method and generalized Halanay inequality, the error level is estimated, a new lag quasi-synchronization scheme is proposed to ensure that coupled memristor-based neural networks are in a state of lag synchronization with an error level. Secondly, by constructing Lyapunov functional and applying common Halanary inequality, several lag complete synchronization criteria for the memristor-based neural networks with parameter match are given, which are easy to verify. Finally, two examples are given to illustrate the effectiveness of the proposed lag quasi-synchronization or lag complete synchronization criteria, which well support theoretical results.

Gβ Regulates Coupling between Actin Oscillators for Cell Polarity and Directional Migration

For directional movement, eukaryotic cells depend on the proper organization of their actin cytoskeleton. This engine of motility is made up of highly dynamic nonequilibrium actin structures such as flashes, oscillations, and traveling waves. In Dictyostelium, oscillatory actin foci interact with signals such as Ras and phosphatidylinositol 3,4,5-trisphosphate (PIP₃) to form protrusions. However, how signaling cues tame actin dynamics to produce a pseudopod and guide cellular motility is a critical open question in eukaryotic chemotaxis. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. We implement an inducible sequestration system to inactivate the heterotrimeric G protein subunit Gβ and find that this acute perturbation triggers persistent, high-amplitude cortical oscillations of F-actin. Actin oscillators that are normally weakly coupled to one another in wild-type cells become strongly synchronized following acute inactivation of Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. A simple mathematical model of coupled actin oscillators reveals the importance of appropriate coupling strength for chemotaxis: moderate coupling can increase sensitivity to noisy inputs. Taken together, our data suggest that Gβ regulates the strength of coupling between actin oscillators for efficient polarity and directional migration. As these observations are only possible following acute inhibition of Gβ and are masked by slow compensation in genetic knockouts, our work also shows that acute loss-of-function approaches can complement and extend the reach of classical genetics in Dictyostelium and likely other systems as well.

Coupling of individual oscillators regulates biological functions ranging from crickets chirping in unison to the coordination of pacemaker cells of the heart. This study finds that a similar concept—coupling between actin oscillators—is at work within single slime mold cells to establish polarity and guide their direction of migration.

The actin cytoskeleton of motile cells is comprised of highly dynamic structures. Recently, small oscillating actin foci have been discovered around the periphery of Dictyostelium cells. These oscillators are thought to enable pseudopod formation, but how their dynamics are regulated for this is unknown. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. Actin oscillators are weakly coupled to one another in wild-type cells, but they become strongly synchronized after acute inactivation of the signaling protein Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. Supported by a mathematical model, our data suggest that wild-type cells are tuned to an optimal coupling strength for patterning by upstream cues. These observations are only possible following acute inhibition of Gβ, which highlights the value of revisiting classical mutants with acute loss-of-function perturbations.

Coherence between Rat Sensorimotor System and Hippocampus Is Enhanced during Tactile Discrimination

Rhythms with time scales of multiple cycles per second permeate the mammalian brain, yet neuroscientists are not certain of their functional roles. One leading idea is that coherent oscillation between two brain regions facilitates the exchange of information between them. In rats, the hippocampus and the vibrissal sensorimotor system both are characterized by rhythmic oscillation in the theta range, 5–12 Hz. Previous work has been divided as to whether the two rhythms are independent or coherent. To resolve this question, we acquired three measures from rats—whisker motion, hippocampal local field potential (LFP), and barrel cortex unit firing—during a whisker-mediated texture discrimination task and during control conditions (not engaged in a whisker-mediated memory task). Compared to control conditions, the theta band of hippocampal LFP showed a marked increase in power as the rats approached and then palpated the texture. Phase synchronization between whisking and hippocampal LFP increased by almost 50% during approach and texture palpation. In addition, a greater proportion of barrel cortex neurons showed firing that was phase-locked to hippocampal theta while rats were engaged in the discrimination task. Consistent with a behavioral consequence of phase synchronization, the rats identified the texture more rapidly and with lower error likelihood on trials in which there was an increase in theta-whisking coherence at the moment of texture palpation. These results suggest that coherence between the whisking rhythm, barrel cortex firing, and hippocampal LFP is augmented selectively during epochs in which the rat collects sensory information and that such coherence enhances the efficiency of integration of stimulus information into memory and decision-making centers.

In rats, the rhythms of whisking and hippocampal theta become coherent precisely when rats approach and explore a texture; higher coherence enhances the identification of texture.

Many regions of the mammalian brain exhibit oscillations in electrical activity. In rats, the 5–12 Hz theta rhythm is present in the hippocampus and in diverse areas of the cerebral cortex. What is the function of this rhythm? One proposal is that the exchange of information between two brain regions is facilitated whenever their respective oscillations are coherent. To test this idea, we ask whether theta oscillation in the hippocampus, a crucial memory structure located deep in the brain, is coherent with the rat’s rhythm of moving its whiskers and sensing the physical environment with them. We acquired hippocampal local field potentials (LFP)—extracellular voltage fluctuations within a small volume—while rats classified textures using cyclical whisker motion (“whisking”). At the moment of texture palpation, coherence between whisking and hippocampal theta oscillations increased by nearly 50%. At the same time, neuronal firing in sensory cortex became more phase-locked to the hippocampal theta oscillations. Rats identified the texture more rapidly and with lower error likelihood on trials characterized by an increase in hippocampal theta-whisking coherence during texture palpation. These results suggest that, as rats collect touch signals, enhanced coherence between the whisking rhythm, sensory cortex, and hippocampal LFP facilitates the integration of sensory information into memory and decision-making centers in the brain.

Electric-field-induced weakly chaotic transients in ferroelectric liquid crystals

Nonlinear dynamics induced in surface stabilized ferroelectric liquid crystals by strong alternating external electric fields is studied both theoretically and experimentally. As has already been shown, molecular reorientations induced by sufficiently strong fields of high-enough frequencies can reveal a long transient behavior that has a weakly chaotic character. The resulting complex dynamics of ferroelectric liquid crystals can be considered not only as a consequence of irregular motions of particular molecules but also as a repercussion of a surface-enforced partial decorrelation of nonlinear molecular motions within smectic layers. To achieve more insight into the nature of this phenomenon and to show that the underlying complex field-induced behavior of smectic liquid crystals is not exceptional, ranges of system parameters for which the chaotic behavior occurs are determined. It is proved that there exists a large enough set of initial phase trajectory points, for which weakly chaotic long-time transitory phenomena occur, and, thereby, it is demonstrated that such a chaotic behavior can be regarded as being typical for strongly field-driven thin liquid crystal systems. Additionally, the influence of low-amplitude random noise on the duration of the transient processes is numerically studied. The strongly nonlinear contribution to the electro-optic response, experimentally determined for liquid crystal samples at frequencies lower than the actual field frequency, is also analyzed for long-time signal sequences. Using a statistical approach to distinguish numerically response signals of samples from noise generated by measuring devices, it is shown that the distribution of sample signals distinctly differs from the device noise. This evidently corroborates the occurrence of the nonlinear low-frequency effect, found earlier for different surface stabilized liquid crystal samples.

The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators

A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a "wideband synchronization channel" in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.

Nonlinear dynamics induced anomalous Hall effect in topological insulators

We uncover an alternative mechanism for anomalous Hall effect. In particular, we investigate the magnetisation dynamics of an insulating ferromagnet (FM) deposited on the surface of a three-dimensional topological insulator (TI), subject to an external voltage. The spin-polarised current on the TI surface induces a spin-transfer torque on the magnetisation of the top FM while its dynamics can change the transmission probability of the surface electrons through the exchange coupling and hence the current. We find a host of nonlinear dynamical behaviors including multistability, chaos, and phase synchronisation. Strikingly, a dynamics mediated Hall-like current can arise, which exhibits a nontrivial dependence on the channel conductance. We develop a physical understanding of the mechanism that leads to the anomalous Hall effect. The nonlinear dynamical origin of the effect stipulates that a rich variety of final states exist, implying that the associated Hall current can be controlled to yield desirable behaviors. The phenomenon can find applications in Dirac-material based spintronics.

Multi-Dimensional Dynamics of Human Electromagnetic Brain Activity

Magnetoencephalography (MEG) and electroencephalography (EEG) are invaluable neuroscientific tools for unveiling human neural dynamics in three dimensions (space, time, and frequency), which are associated with a wide variety of perceptions, cognition, and actions. MEG/EEG also provides different categories of neuronal indices including activity magnitude, connectivity, and network properties along the three dimensions. In the last 20 years, interest has increased in inter-regional connectivity and complex network properties assessed by various sophisticated scientific analyses. We herein review the definition, computation, short history, and pros and cons of connectivity and complex network (graph-theory) analyses applied to MEG/EEG signals. We briefly describe recent developments in source reconstruction algorithms essential for source-space connectivity and network analyses. Furthermore, we discuss a relatively novel approach used in MEG/EEG studies to examine the complex dynamics represented by human brain activity. The correct and effective use of these neuronal metrics provides a new insight into the multi-dimensional dynamics of the neural representations of various functions in the complex human brain.

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks.

Detection of Coupling in Short Physiological Series by a Joint Distribution Entropy Method

OBJECTIVE

In this study, we developed a joint distribution entropy (JDistEn) method to robustly estimate the coupling in short physiological series.

METHODS

The JDistEn method is derived from a joint distance matrix which is constructed from a combination of the distance matrix corresponding to each individual data channel using a geometric mean calculation. A coupled Rössler system and a coupled dual-kinetics neural mass model were used to examine how well JDistEn performed, specifically, its sensitivity for detecting weak coupling, its consistency in gauging coupling strength, and its reliability in processing input of decreased data length. Performance of JDistEn in estimating physiological coupling was further examined with bivariate electroencephalography data from rats and RR interval and diastolic time interval series from human beings. Cross-sample entropy (XSampEn), cross-conditional entropy (XCE), and Shannon entropy of diagonal lines in the joint recurrence plots (JENT) were applied for purposes of comparison.

RESULTS

Simulation results suggest that JDistEn showed markedly higher sensitivity than XSampEn, XCE, and JENT for dynamics in weak coupling, although as the simulation models were more intensively coupled, JDistEn performance was comparable to the three others. In addition, this improved sensitivity was much more pronounced for short datasets. Experimental results further confirmed that JDistEn outperformed XSampEn, XCE, and JENT for detecting weak coupling, especially for short physiological data.

CONCLUSION

This study suggested that our proposed JDistEn could be useful for continuous and even real-time coupling analysis for physiological signals in clinical practice.

Mutual regulation causes co-entrainment between a synthetic oscillator and the bacterial cell cycle

The correct functioning of cells requires the orchestration of multiple cellular processes, many of which are inherently dynamical. The conditions under which these dynamical processes entrain each other remain unclear. Here we use synthetic biology to address this question in the case of concurrent cellular oscillations. Specifically, we study at the single-cell level the interaction between the cell division cycle and a robust synthetic gene oscillator in Escherichia coli. Our results suggest that cell division is able to partially entrain the synthetic oscillations under normal growth conditions, by driving the periodic replication of the genes involved in the oscillator. Coupling the synthetic oscillations back into the cell cycle via the expression of a key regulator of chromosome replication increases the synchronization between the two periodic processes. A simple computational model allows us to confirm this effect.