Phase synchronization of chaotic oscillators

One node driving synchronisation

Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with heterogeneous coupling strengths. The synchronisation of phase-oscillators is independent of the distribution of the natural frequencies, weakly depends on the network size, but highly depends on only one key oscillator whose ratio between its natural frequency in a rotating frame and its coupling strength is maximum. This result is based on a novel method to calculate the critical coupling strength with which the phase-oscillators emerge into frequency synchronisation. In addition, we put forward an analytical method to approximately calculate the phase-angles for the synchronous oscillators.

Effects of Spike Anticipation on the Spiking Dynamics of Neural Networks

Synchronization is one of the central phenomena involved in information processing in living systems. It is known that the nervous system requires the coordinated activity of both local and distant neural populations. Such an interplay allows to merge different information modalities in a whole processing supporting high-level mental skills as understanding, memory, abstraction, etc. Though, the biological processes underlying synchronization in the brain are not fully understood there have been reported a variety of mechanisms supporting different types of synchronization both at theoretical and experimental level. One of the more intriguing of these phenomena is the anticipating synchronization, which has been recently reported in a pair of unidirectionally coupled artificial neurons under simple conditions (Pyragiene and Pyragas, 2013), where the slave neuron is able to anticipate in time the behavior of the master one. In this paper, we explore the effect of spike anticipation over the information processing performed by a neural network at functional and structural level. We show that the introduction of intermediary neurons in the network enhances spike anticipation and analyse how these variations in spike anticipation can significantly change the firing regime of the neural network according to its functional and structural properties. In addition we show that the interspike interval (ISI), one of the main features of the neural response associated with the information coding, can be closely related to spike anticipation by each spike, and how synaptic plasticity can be modulated through that relationship. This study has been performed through numerical simulation of a coupled system of Hindmarsh–Rose neurons.

Amplified response in coupled chaotic oscillators by induced heterogeneity

The phenomenon of emergent amplified response is reported in two unidirectionally coupled identical chaotic systems when heterogeneity as a parameter mismatch is introduced in a state of complete synchrony. The amplified response emerges from the interplay of heterogeneity and a type of cross-feedback coupling. It is reflected as an expansion of the response attractor in some directions in the state space of the coupled system. The synchronization manifold is simply rotated by the parameter detuning while its stability in the transverse direction is still maintained. The amplification factor is linearly related to the amount of parameter detuning. The phenomenon is elaborated with examples of the paradigmatic Lorenz system, the Shimizu-Morioka single-mode laser model, the Rössler system, and a Sprott system. Experimental evidence of the phenomenon is obtained in an electronic circuit. The method may provide an engineering tool for distortion-free amplification of chaotic signals.

Approximate solution for frequency synchronization in a finite-size Kuramoto model

Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behavior, such as frequency synchronization (FS) as a paradigm, in real-world networks with a finite number of oscillators. A major current challenge is to obtain an analytical solution for the phase angles. Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, with arbitrary finite-variance distribution of the natural frequencies of the oscillators. The master solution embodies all particular solutions of the finite-size Kuramoto model for any frequency distribution and coupling strength larger than the critical one. Furthermore, we present a criterion to determine the stability of the FS solution. This allows one to analytically infer the relationship between the physical parameters and the stable behavior of networks.

Experimental Study of the Triplet Synchronization of Coupled Nonidentical Mechanical Metronomes

Triplet synchrony is an interesting state when the phases and the frequencies of three coupled oscillators fulfill the conditions of a triplet locking, whereas every pair of systems remains asynchronous. Experimental observation of triplet synchrony is firstly realized in three coupled nonidentical mechanical metronomes. A more direct method based on the phase diagram is proposed to observe and determine triplet synchronization. Our results show that the stable triplet synchrony is observed in several intervals of the parameter space. Moreover, the experimental results are verified according to the theoretical model of the coupled metronomes. The outcomes are useful to understand the inner regimes of collective dynamics in coupled oscillators.

Function projective synchronization of memristor-based Cohen-Grossberg neural networks with time-varying delays

This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen-Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.

Synchronization of Heterogeneous Oscillators by Noninvasive Time-Delayed Cross Coupling

We demonstrate that nonidentical systems, in particular, nonlinear oscillators with different time scales, can be synchronized if a mutual coupling via time-delayed control signals is implemented. Each oscillator settles on an unstable state, say a fixed point or an unstable periodic orbit, with a coupling force which vanishes in the long time limit. We present the underlying theoretical considerations and numerical simulations, and, moreover, demonstrate the concept experimentally in nonlinear electronic oscillators.

Synchronization of nearly identical dynamical systems: Size instability

We study the generalized synchronization and its stability using the master stability function (MSF) in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling matrix. Using the MSF we study the size instability in star and ring networks for coupled nearly identical dynamical systems. In the star network of coupled Rössler systems we show that the critical size beyond which synchronization is unstable can be increased by having a larger frequency for the central node of the star. For the ring network we show that the critical size is not significantly affected by parameter variations. The results are verified by explicit numerical calculations.

Revival of oscillation from mean-field-induced death: Theory and experiment

The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological, and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in Zou et al. [Nat. Commun. 6, 7709 (2015)], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean field is capable of inducing rhythmicity even in the presence of complete diffusion, which is a unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results.

Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch

A small mismatch between natural frequencies of unidirectionally coupled chaotic oscillators can induce coherence resonance in the slave oscillator for a certain coupling strength. This surprising phenomenon resembles "stabilization of chaos by chaos," i.e., the chaotic driving applied to the chaotic system makes its dynamics more regular when the natural frequency of the slave oscillator is a little different than the natural frequency of the master oscillator. The coherence is characterized with the dominant component in the power spectrum of the slave oscillator, normalized standard deviations of both the peak amplitude and the interpeak interval, and Lyapunov exponents. The enhanced coherence is associated with increasing negative both the third and the fourth Lyapunov exponents, while the first and second exponents are always positive and zero, respectively.

Switching synchronization in one-dimensional memristive networks

We report on a switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high- to low-resistance state. Our numerical simulations show that such a collective behavior is especially pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. Moreover, a finite increase in the network switching time is found compared to the average switching time of individual systems. An analytical model is presented to explain our observations. Using this model, we have derived asymptotic expressions for memory resistances at short and long times, which are in excellent agreement with results of our numerical simulations.

Disrupted Ipsilateral Network Connectivity in Temporal Lobe Epilepsy

OBJECTIVE

The current practice under which patients with refractory epilepsy are surgically treated is based mainly on the identification of specific cortical areas, mainly the epileptogenic zone, which is believed to be responsible for generation of seizures. A better understanding of the whole epileptic network and its components and properties is required before more effective and less invasive therapies can be developed. The aim of the present study was to partially characterize the evolution of the functional network during the preictal-ictal transition in partial seizures in patients with temporal lobe epilepsy (TLE).

METHODS

Scalp and foramen ovale (FOE) recordings from twenty-two TLE patients were analyzed under the complex network perspective. The density of links, average path length, average clustering coefficient, and modularity were calculated during the preictal and the ictal stages. Both linear-Pearson correlation-and non-linear-phase synchronization-measures were used as proxies of functional connectivity between the electrode locations areas. The transition from one stage to the other was evaluated in the whole network and in the mesial sub-networks. The results were compared with a voltage-dependent measure, namely, the spectral entropy.

RESULTS

Changes in the global functional network during the transition from the preictal to the ictal stage show, in the linear case, that in sixteen cases (72.7%) the density of the links increased during the seizure, with a decrease in the average path length in fifteen cases (68.1%). There was also a preictal and ictal imbalance in functional connectivity during both stages (77.2% to 86.3%). The SE dropped during the seizure in 95.4% of the cases, but did not show any tendency towards lateralization. When using the nonlinear measure of functional connectivity, the phase synchronization, similar results were obtained.

CONCLUSIONS

In TLE patients, the transition to the ictal stage is accompanied by increasing global synchronization and a more ordered spectral content of the signals, indicated by lower spectral entropy. The interictal connectivity imbalance (lower ipsilateral connectivity) is sustained during the seizure, irrespective of any appreciable imbalance in the spectral entropy of the mesial recordings.

Dynamics of globally coupled oscillators: Progress and perspectives

In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.

A General Approach for Quantifying Nonlinear Connectivity in the Nervous System Based on Phase Coupling

Interaction between distant neuronal populations is essential for communication within the nervous system and can occur as a highly nonlinear process. To better understand the functional role of neural interactions, it is important to quantify the nonlinear connectivity in the nervous system. We introduce a general approach to measure nonlinear connectivity through phase coupling: the multi-spectral phase coherence (MSPC). Using simulated data, we compare MSPC with existing phase coupling measures, namely n : m synchronization index and bi-phase locking value. MSPC provides a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling beyond the second order; which are only partly revealed by other methods. We apply MSPC to analyze data from a motor control experiment, where subjects performed isotonic wrist flexions while receiving movement perturbations. MSPC between the perturbation, EEG and EMG was calculated. Our results reveal directional nonlinear connectivity in the afferent and efferent pathways, as well as the time delay (43 ± 8 ms) between the perturbation and the brain response. In conclusion, MSPC is a novel approach capable to assess high-order nonlinear interaction and timing in the nervous system.

Synchronization-based computation through networks of coupled oscillators

The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.

Transient Uncoupling Induces Synchronization

Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently uncoupling them. Specifically, systems coupled only in a fraction of their state space may synchronize even if fully coupled they do not. While for many standard systems coupling strengths need to be bounded to ensure synchrony, transient uncoupling removes this bound and thus enables synchronization in an infinite range of effective coupling strengths. The presented coupling scheme therefore opens up the possibility to induce synchrony in (biological or technical) systems whose parameters are fixed and cannot be modified continuously.

Intrinsic coupling modes in source-reconstructed electroencephalography

Intrinsic coupling of neuronal assemblies constitutes a key feature of ongoing brain activity, yielding the rich spatiotemporal patterns observed in neuroimaging data and putatively supporting cognitive processes. Intrinsic coupling has been investigated in electrophysiological recordings using two types of functional connectivity measures: amplitude and phase coupling. These two coupling modes differ in their likely causes and functions, and have been proposed to provide complementary insights into intrinsic neuronal interactions. Here, we investigate the relationship between amplitude and phase coupling in source-reconstructed electroencephalography (EEG). Volume conduction is a key obstacle for connectivity analysis in EEG-we therefore also test the envelope correlation of orthogonalized signals and the phase lag index. Functional connectivity between six seed source regions (bilateral visual, sensorimotor, and auditory cortices) and all other cortical voxels was computed. For all four measures, coupling between homologous sensory areas in both hemispheres was significantly higher than with other voxels at the same physical distance. The frequency of significant coupling differed between sensory areas: 10 Hz for visual, 30 Hz for auditory, and 40 Hz for sensorimotor cortices. By contrasting envelope correlations and phase locking values, we observed two distinct clusters of voxels showing a different relationship between amplitude and phase coupling. Large clusters contiguous to the seed regions showed an identity (1:1) relationship between amplitude and phase coupling, whereas a cluster located around the contralateral homologous regions showed higher phase than amplitude coupling. These results show a relationship between intrinsic coupling modes that is distinct from the effect of volume conduction.

Two types of quasiperiodic partial synchrony in oscillator ensembles

We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different quasiperiodic states. We present an example of a bifurcation diagram, where we show the borderlines for all these transitions, as well as domain of bistability.

Rapid brief feedback intracerebral stimulation based on real-time desynchronization detection preceding seizures stops the generation of convulsive paroxysms

OBJECTIVE

To investigate the abortion of seizure generation using "minimal" intervention in hippocampi using two rat models of human temporal lobe epilepsy.

METHODS

The recording or stimulation electrodes were implanted into both hippocampi (CA1 area). Using the kainic acid (chronic: experiment duration 24 days) and the 4-aminopyridine (acute: experiment duration 2 h) models of paroxysms in rats, a real-time feedback stimulation paradigm was implemented, which triggered a short periodic electrical stimulus (5 Hz for 5 s) upon detecting a seizure precursor. Our seizure precursor detection algorithm relied on the monitoring of the real-time phase synchronization analysis, and detected/anticipated electrographic seizures as early as a few seconds to a few minutes before the behavioral and electrographic seizure onset, with a very low false-positive rate of the detection.

RESULTS

The baseline mean seizure frequencies were 5.39 seizures per day (chronic) and 13.2 seizures per hour (acute). The phase synchrony analysis detected 88% (434 of 494) of seizures with a mean false alarm of 0.67 per day (chronic) and 83% (86 of 104) of seizures with a mean false alarm of 0.47 per hour (acute). The feedback stimulation reduced the seizure frequencies to 0.41 seizures per day (chronic) and 2.4 seizures per hour (acute). Overall, the feedback stimulation paradigm reduced seizure frequency by a minimum of 80% to a maximum of 100% in 10 rats, with 83% of the animals rendered seizure-free.

SIGNIFICANCE

This approach represents a simple and efficient manner for stopping seizure development. Because of the short on-demand stimuli, few or no associated side effects are expected in clinical application in patients with epilepsy. Abnormal synchrony patterns are common features in epilepsy and other neurologic and psychiatric syndromes; therefore, this type of feedback stimulation paradigm could be a novel therapeutic modality for use in various neurologic and psychiatric disorders.

What graph theory actually tells us about resting state interictal MEG epileptic activity

Graph theory provides a useful framework to study functional brain networks from neuroimaging data. In epilepsy research, recent findings suggest that it offers unique insight into the fingerprints of this pathology on brain dynamics. Most studies hitherto have focused on seizure activity during focal epilepsy, but less is known about functional epileptic brain networks during interictal activity in frontal focal and generalized epilepsy. Besides, it is not clear yet which measures are most suitable to characterize these networks. To address these issues, we recorded magnetoencephalographic (MEG) data using two orthogonal planar gradiometers from 45 subjects from three groups (15 healthy controls (7 males, 24 ± 6 years), 15 frontal focal (8 male, 32 ± 16 years) and 15 generalized epileptic (6 male, 27 ± 7 years) patients) during interictal resting state with closed eyes. Then, we estimated the total and relative spectral power of the largest principal component of the gradiometers, and the degree of phase synchronization between each sensor site in the frequency range [0.5–40 Hz]. We further calculated a comprehensive battery of 15 graph-theoretic measures and used the affinity propagation clustering algorithm to elucidate the minimum set of them that fully describe these functional brain networks. The results show that differences in spectral power between the control and the other two groups have a distinctive pattern: generalized epilepsy presents higher total power for all frequencies except the alpha band over a widespread set of sensors; frontal focal epilepsy shows higher relative power in the beta band bilaterally in the fronto-central sensors. Moreover, all network indices can be clustered into three groups, whose exemplars are the global network efficiency, the eccentricity and the synchronizability. Again, the patterns of differences were clear: the brain network of the generalized epilepsy patients presented greater efficiency and lower eccentricity than the control subjects for the high frequency bands, without a clear topography. Besides, the frontal focal epileptic patients showed only reduced eccentricity for the theta band over fronto-temporal and central sensors. These outcomes indicate that functional epileptic brain networks are different to those of healthy subjects during interictal stage at rest, with a unique pattern of dissimilarities for each type of epilepsy. Further, when properly selected, three network indices suffice to provide a comprehensive description of these differences. Yet, since such uniqueness in the pattern of differences is also evident in the power spectrum, we conclude that the added value of the graph theory approach in this context should not be overestimated.

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We study MEG activity during interictal resting state with closed eyes.

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Generalized epilepsy presents higher total power over a widespread set of sensors.

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Frontal epilepsy shows higher relative power in beta band on fronto-central sensors.

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We also found altered functional brain networks in epilepsy using graph theory.

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The pattern of differences from control subjects is unique for each type of epilepsy.

Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators

The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.

Entrainment of heterogeneous glycolytic oscillations in single cells

Cell signaling, gene expression, and metabolism are affected by cell-cell heterogeneity and random changes in the environment. The effects of such fluctuations on cell signaling and gene expression have recently been studied intensively using single-cell experiments. In metabolism heterogeneity may be particularly important because it may affect synchronisation of metabolic oscillations, an important example of cell-cell communication. This synchronisation is notoriously difficult to describe theoretically as the example of glycolytic oscillations shows: neither is the mechanism of glycolytic synchronisation understood nor the role of cell-cell heterogeneity. To pin down the mechanism and to assess its robustness and universality we have experimentally investigated the entrainment of glycolytic oscillations in individual yeast cells by periodic external perturbations. We find that oscillatory cells synchronise through phase shifts and that the mechanism is insensitive to cell heterogeneity (robustness) and similar for different types of external perturbations (universality).

Salient features of otoacoustic emissions are common across tetrapod groups and suggest shared properties of generation mechanisms

Otoacoustic emissions (OAEs) are faint sounds generated by healthy inner ears that provide a window into the study of auditory mechanics. All vertebrate classes exhibit OAEs to varying degrees, yet the biophysical origins are still not well understood. Here, we analyzed both spontaneous (SOAE) and stimulus-frequency (SFOAE) otoacoustic emissions from a bird (barn owl, Tyto alba) and a lizard (green anole, Anolis carolinensis). These species possess highly disparate macromorphologies of the inner ear relative to each other and to mammals, thereby allowing for novel insights into the biomechanical mechanisms underlying OAE generation. All ears exhibited robust OAE activity, and our chief observation was that SFOAE phase accumulation between adjacent SOAE peak frequencies clustered about an integral number of cycles. Being highly similar to published results from human ears, we argue that these data indicate a common underlying generator mechanism of OAEs across all vertebrates, despite the absence of morphological features thought essential to mammalian cochlear mechanics. We suggest that otoacoustic emissions originate from phase coherence in a system of coupled oscillators, which is consistent with the notion of "coherent reflection" but does not explicitly require a mammalian-type traveling wave. Furthermore, comparison between SFOAE delays and auditory nerve fiber responses for the barn owl strengthens the notion that most OAE delay can be attributed to tuning.

Synchronization in an optomechanical cavity

We study self-excited oscillations (SEO) in an on-fiber optomechanical cavity. Synchronization is observed when the optical power that is injected into the cavity is periodically modulated. A theoretical analysis based on the Fokker-Planck equation evaluates the expected phase space distribution (PSD) of the self-oscillating mechanical resonator. A tomography technique is employed for extracting PSD from the measured reflected optical power. Time-resolved state tomography measurements are performed to study phase diffusion and phase locking of the SEO. The detuning region inside which synchronization occurs is experimentally determined and the results are compared with the theoretical prediction.

Synchronization in stress p53 network

We study transition of the temporal behaviours of p53 and MDM2 in a stress p53-MDM2-NO regulatory network induced by a bioactive molecule NO (Nitric Oxide). We further study synchronization among a group of identical stress systems arranged in a 3D array with nearest neighbour diffusive coupling. The role of NO and the effect of noise are investigated. In the single system study, we found three distinct types of temporal behaviour of p53, namely oscillation death, damped oscillation and sustained oscillation, depending on the amount of stress induced by NO, indicating how p53 responds to incoming stress. The correlation among coupled systems increases as the value of the coupling constant (ϵ) is increased (γ increases) and becomes constant after a certain value of ϵ. The permutation entropy spectra H(ϵ) for p53 and MDM2 as a function of ϵ are found to be different due to direct and indirect interaction of NO with respective proteins. We find γ versus ϵ for p53 and MDM2 to be similar in a deterministic approach but different in a stochastic approach, and the separation between γ of the respective proteins as a function of ϵ decreases as system size increases. The role of NO is found to be two-fold: stress induced by NO is prominent at small and large values of ϵ but synchrony induced by it dominates in the moderate range of ϵ. Excess stress induces apoptosis.

Synaptic plasticity-related neural oscillations on hippocampus-prefrontal cortex pathway in depression

It is believed that phase synchronization facilitates neural communication and neural plasticity throughout the hippocampal-cortical network, and further supports cognition and memory. The pathway from the ventral hippocampus to the medial prefrontal cortex (mPFC) is thought to play a significant role in emotional memory processing. Therefore, the information transmission on the pathway was hypothesized to be disrupted in the depressive state, which could be related to its impaired synaptic plasticity. In this study, local field potentials (LFPs) from both ventral CA1 (vCA1) and mPFC were recorded in both normal and chronic unpredictable stress (CUS) model rats under urethane anesthesia. LFPs of all rats were recorded before and after the long-term potentiation (LTP) induced on the vCA1-mPFC pathway in order to figure out the correlation of oscillatory synchronization of LFPs and synaptic plasticity. Our results showed the vCA1-to-mPFC unidirectional phase coupling of the theta rhythm, rather than the power of either region, was significantly enhanced by LTP induction, with less enhancement in the CUS model rats compared to that in the normal rats. In addition, theta phase coupling was positively correlated with synaptic plasticity on vCA1-mPFC pathway. Moreover, the theta-slow gamma phase-amplitude coupling in vCA1 was long-term enhanced after high frequency stimulation. These results suggest that the impaired synaptic plasticity in vCA1-mPFC pathway could be reflected by the attenuated theta phase coupling and theta-gamma cross frequency coupling of LFPs in the depression state.

Individual differences in attention influence perceptual decision making

Sequential sampling decision-making models have been successful in accounting for reaction time (RT) and accuracy data in two-alternative forced choice tasks. These models have been used to describe the behavior of populations of participants, and explanatory structures have been proposed to account for between individual variability in model parameters. In this study we show that individual differences in behavior from a novel perceptual decision making task can be attributed to (1) differences in evidence accumulation rates, (2) differences in variability of evidence accumulation within trials, and (3) differences in non-decision times across individuals. Using electroencephalography (EEG), we demonstrate that these differences in cognitive variables, in turn, can be explained by attentional differences as measured by phase-locking of steady-state visual evoked potential (SSVEP) responses to the signal and noise components of the visual stimulus. Parameters of a cognitive model (a diffusion model) were obtained from accuracy and RT distributions and related to phase-locking indices (PLIs) of SSVEPs with a single step in a hierarchical Bayesian framework. Participants who were able to suppress the SSVEP response to visual noise in high frequency bands were able to accumulate correct evidence faster and had shorter non-decision times (preprocessing or motor response times), leading to more accurate responses and faster response times. We show that the combination of cognitive modeling and neural data in a hierarchical Bayesian framework relates physiological processes to the cognitive processes of participants, and that a model with a new (out-of-sample) participant's neural data can predict that participant's behavior more accurately than models without physiological data.

Impact of a leader on cluster synchronization

We study the mechanisms of frequency-synchronized cluster formation in coupled nonidentical oscillators and investigate the impact of presence of a leader on the cluster synchronization. We find that the introduction of a leader, a node having large parameter mismatch, induces a profound change in the cluster pattern as well as in the mechanism of the cluster formation. The emergence of a leader generates a transition from the driven to the mixed cluster state. The frequency mismatch turns out to be responsible for this transition. Additionally, for a chaotic evolution, the driven mechanism stands as a primary mechanism for the cluster formation, whereas for a periodic evolution the self-organization mechanism becomes equally responsible.

Input-dependent frequency modulation of cortical gamma oscillations shapes spatial synchronization and enables phase coding

Fine-scale temporal organization of cortical activity in the gamma range (∼25-80Hz) may play a significant role in information processing, for example by neural grouping ('binding') and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity.

Emergent hybrid synchronization in coupled chaotic systems

We evidence an interesting kind of hybrid synchronization in coupled chaotic systems where complete synchronization is restricted to only a subset of variables of two systems while other subset of variables may be in a phase synchronized state or desynchronized. Such hybrid synchronization is a generic emergent feature of coupled systems when a controller based coupling, designed by the Lyapunov function stability, is first engineered to induce complete synchronization in the identical case, and then a large parameter mismatch is introduced. We distinguish between two different hybrid synchronization regimes that emerge with parameter perturbation. The first, called hard hybrid synchronization, occurs when the coupled systems display global phase synchronization, while the second, called soft hybrid synchronization, corresponds to a situation where, instead, the global synchronization feature no longer exists. We verify the existence of both classes of hybrid synchronization in numerical examples of the Rössler system, a Lorenz-like system, and also in electronic experiment.

The relevance of the cross-wavelet transform in the analysis of human interaction - a tutorial

This article sheds light on a quantitative method allowing psychologists and behavioral scientists to take into account the specific characteristics emerging from the interaction between two sets of data in general and two individuals in particular. The current article outlines the practical elements of the cross-wavelet transform (CWT) method, highlighting WHY such a method is important in the analysis of time-series in psychology. The idea is (1) to bridge the gap between physical measurements classically used in physiology - neuroscience and psychology; (2) and demonstrates how the CWT method can be applied in psychology. One of the aims is to answer three important questions WHO could use this method in psychology, WHEN it is appropriate to use it (suitable type of time-series) and HOW to use it. Throughout these explanations, an example with simulated data is used. Finally, data from real life application are analyzed. This data corresponds to a rating task where the participants had to rate in real time the emotional expression of a person. The objectives of this practical example are (i) to point out how to manipulate the properties of the CWT method on real data, (ii) to show how to extract meaningful information from the results, and (iii) to provide a new way to analyze psychological attributes.

State feedback-based secure image cryptosystem using hyperchaotic synchronization

This paper deals with a new state feedback-based synchronization problem for coupled hyperchaotic systems. In the beginning, complete synchronization conditions of coupled chaotic systems, are provided. The active control law developed is based on the use of both aggregation techniques for error dynamics stability study and the arrow form matrix for systems description. After that, the proposed feedback-based synchronization between two identical hyperchaotic systems is successfully applied for transmitting an encoded image. To finish, numerical simulations are carried out to assess the performance and the efficiency of the proposed contributions in the important field of secure image encryption.

The discrete complex wavelet approach to phase assignment and a new test bed for related methods

A new approach based on the dual-tree complex wavelet transform is introduced for phase assignment to non-linear oscillators, namely, the Discrete Complex Wavelet Approach-DCWA. This methodology is able to measure phase difference with enough accuracy to track fine variations, even in the presence of Gaussian observational noise and when only a single scalar measure of the oscillator is available. So, it can be an especially interesting tool to deal with experimental data. In order to compare it with other phase detection techniques, a testbed is introduced. This testbed provides time series from dynamics similar to non-linear oscillators, such that a theoretical phase choice is known in advance. Moreover, it allows to tune different types of phase synchronization to test phase detection methods under a variety of scenarios. Through numerical benchmarks, we report that the proposed approach is a reliable alternative and that it is particularly effective compared with other methodologies in the presence of moderate to large noises.

Characterization of topographically specific sleep spindles in mice

STUDY OBJECTIVE

Sleep spindles in humans have been classified as slow anterior and fast posterior spindles; recent findings indicate that their profiles differ according to pharmacology, pathology, and function. However, little is known about the generation mechanisms within the thalamocortical system for different types of spindles. In this study, we aim to investigate the electrophysiological behaviors of the topographically distinctive spindles within the thalamocortical system by applying high-density EEG and simultaneous thalamic LFP recordings in mice.

DESIGN

32-channel extracranial EEG and 2-channel thalamic LFP were recorded simultaneously in freely behaving mice to acquire spindles during spontaneous sleep.

SUBJECTS

Hybrid F1 male mice of C57BL/6J and 129S4/svJae.

MEASUREMENTS AND RESULTS

Spindle events in each channel were detected by spindle detection algorithm, and then a cluster analysis was applied to classify the topographically distinctive spindles. All sleep spindles were successfully classified into 3 groups: anterior, posterior, and global spindles. Each spindle type showed distinct thalamocortical activity patterns regarding the extent of similarity, phase synchrony, and time lags between cortical and thalamic areas during spindle oscillation. We also found that sleep slow waves were likely to associate with all types of sleep spindles, but also that the ongoing cortical decruitment/ recruitment dynamics before the onset of spindles and their relationship with spindle generation were also variable, depending on the spindle types.

CONCLUSION

Topographically specific sleep spindles show distinctive thalamocortical network behaviors.

Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: phase, amplitude, and clustering effects

In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.

Sound synchronization of bubble trains in a viscous fluid: experiment and modeling

We investigate the dynamics of formation of air bubbles expelled from a nozzle immersed in a viscous fluid under the influence of sound waves. We have obtained bifurcation diagrams by measuring the time between successive bubbles, having the air flow (Q) as a parameter control for many values of the sound wave amplitude (A), the height (H) of the solution above the top of the nozzle, and three values of the sound frequency (fs). Our parameter spaces (Q,A) revealed a scenario for the onset of synchronization dominated by Arnold tongues (frequency locking) which gives place to chaotic phase synchronization for sufficiently large A. The experimental results were accurately reproduced by numerical simulations of a model combining a simple bubble growth model for the bubble train and a coupling term with the sound wave added to the equilibrium pressure.

Two intrinsic coupling types for resting-state integration in the human brain

Recent findings indicate that synchronous neural activity at rest influences human performance in subsequent tasks. Synchronization can occur in form of phase coupling or amplitude correlation. It is unknown whether these coupling types have differing behavioral significance at rest. To address this, we performed resting-state electroencephalography (EEG) and source connectivity analysis in several populations of healthy subjects and patients with brain lesions. We systematically compared different types and frequencies of neural synchronization and investigated their association with behavioral performance in verbal and spatial attention tasks. Behavioral performance could be consistently predicted by two distinct resting-state coupling patterns: (1) amplitude envelope correlation of beta activity between homologous areas of both hemispheres, (2) lagged phase synchronization in EEG alpha activity between a brain area and the entire cortex. A disruption of these coupling patterns was also associated with neurological deficits in patients with stroke lesions. This suggests the existence of two distinct network systems responsible for resting-state integration. Lagged phase synchronization in the alpha band is associated with global interaction across networks while amplitude envelope correlation seems to be behaviorally relevant for interactions within networks and between hemispheres. These two coupling types may therefore provide complementary insights on brain physiology and pathology.

Control for a synchronization-desynchronization switch

How to freely enhance or suppress synchronization of networked dynamical systems is of great importance in many disciplines. A unified precise control method for a synchronization-desynchronization switch, called the pull-push control method, is suggested. Namely, synchronization can be achieved when the original systems are desynchronous by pulling (or protecting) one node or a certain subset of nodes, whereas desynchronization can be accomplished when the systems are already synchronous by pushing (or kicking) one node or a certain subset of nodes. With this method, the controlled nodes should be chosen by the generalized eigenvector centrality of the critical synchronization mode of the Laplacian matrix. Compared with existing control methods for synchronization, it displays high efficiency, flexibility, and precision as well.