Signal transmission by vibrational resonance in one-way coupled bistable systems

Vibrational resonance in an asymmetric system modeled by an electronic circuit: Effect of the buffers

Vibrational resonance (VR) has been extensively studied in symmetric circuits, but research on this phenomenon in asymmetric electronic circuits is understudied. The current study aims to model a novel asymmetric electronic circuit and investigate the occurrence of VR in the circuit. This oscillator shows changes according to four control parameters, with the aid of two buffers. The amplification of signals in electronic circuits gives interesting results, vibrational resonance is one of the phenomena which is based on the amplification of signals. In this study, the asymmetric strength caused by the potentiometers and the frequencies influence are the major aims explored. Interestingly, the circuit shows different types of behaviors that are pointed out through waveform profiles, bifurcation diagrams, largest Lyapunov exponent, and the phase portraits. The dynamic of the system is studied theoretically, numerically and by Pspice Simulation. The Pspice estimates match with numerical simulations. We use the response Q(ω) method, based on the sine and cosine of the Fourier component to study VR. Our discovery suggests that the asymmetric parameter and the amplitude of the high frequency, both affect the occurrence of vibrational resonance.

Ultrasensitive vibrational resonance induced by small disturbances

We have found two kinds of ultrasensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultrasensitive vibrational resonance is transient behavior caused by transient chaos. Considering a long-term response, the system will transform from transient chaos to a periodic response. The pattern of vibrational resonance will also transform from ultrasensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultrasensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultrasensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from ultrasensitive vibrational resonance to conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultrasensitive vibrational resonance appears and the plot of the response amplitude vs the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly periodic, it usually corresponds to the conventional vibrational resonance. The ultrasensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultrasensitive vibrational resonance as transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.

Stochastic and vibrational resonance in complex networks of neurons

The concept of resonance in nonlinear systems is crucial and traditionally refers to a specific realization of maximum response provoked by a particular external perturbation. Depending on the system and the nature of perturbation, many different resonance types have been identified in various fields of science. A prominent example is in neuroscience where it has been widely accepted that a neural system may exhibit resonances at microscopic, mesoscopic and macroscopic scales and benefit from such resonances in various tasks. In this context, the two well-known forms are stochastic and vibrational resonance phenomena which manifest that detection and propagation of a feeble information signal in neural structures can be enhanced by additional perturbations via these two resonance mechanisms. Given the importance of network architecture in proper functioning of the nervous system, we here present a review of recent studies on stochastic and vibrational resonance phenomena in neuronal media, focusing mainly on their emergence in complex networks of neurons as well as in simple network structures that represent local behaviours of neuron communities. From this perspective, we aim to provide a secure guide by including theoretical and experimental approaches that analyse in detail possible reasons and necessary conditions for the appearance of stochastic resonance and vibrational resonance in neural systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Vibrational resonance in a neuron-astrocyte coupled model

Recent findings have revealed that not only neurons but also astrocytes, a special type of glial cells, are major players of neuronal information processing. It is now widely accepted that they contribute to the regulation of their microenvironment by cross-talking with neurons via gliotransmitters. In this context, we here study the phenomenon of vibrational resonance in neurons by considering their interaction with astrocytes. Our analysis of a neuron-astrocyte pair reveals that intracellular dynamics of astrocytes can induce a double vibrational resonance effect in the weak signal detection performance of a neuron, exhibiting two distinct wells centred at different high-frequency driving amplitudes. We also identify the underlying mechanism of this behaviour, showing that the interaction of widely separated time scales of neurons, astrocytes and driving signals is the key factor for the emergence and control of double vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.

Anormal diffusion enhancement of resonant responses for coupled oscillator networks to weak signals

The normal diffusion effect is introduced as a new regulating factor into the established diffusive coupling model for bistable oscillator networks. We find that the response of the system to the weak signal is substantially enhanced by the anormal diffusion, which is termed anormal-diffusion-induced resonance. We also reveal that the diffusive coupling-induced transition, which changes the system from a bistable to a monostable state, is of fundamental importance for the occurrence of resonance. The proposed approach is validated using simulation studies and theoretical analyses. Our results suggest that diffusion induced resonance can be more easily observed in nonlinear oscillator networks.

Entropic vibrational resonance

We demonstrate the existence of vibrational resonance associated with the presence of an uneven boundary. When the motion of a Brownian particle is confined in a region with an uneven boundary, constrained to a double cavity, a high-frequency signal may produce a peak in the spectral power amplification of the other low-frequency signal and therefore to the appearance of the vibrational resonance phenomenon. The mechanism of vibrational resonance in constrained boundaries is different from that in energetic potentials and is termed entropic vibrational resonance (EVR). The EVR can be observed even if the bias force is absent in any direction. Through careful analysis, we clarify two types of mechanisms of the EVR. The one mechanism is ascribed to the transition from a bistable system to a monostable system, and the other corresponds to the match between the escape rate and the natural frequency of the low-frequency signal. Our work merges the vibrational resonance with an uneven boundary, thus extending the scope of the vibrational resonance and shedding new light on the concept of resonance.

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh-Nagumo neuron

Based on the FitzHugh-Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.

The role of glutamate in neuronal ion homeostasis: A case study of spreading depolarization

Simultaneous changes in ion concentrations, glutamate, and cell volume together with exchange of matter between cell network and vasculature are ubiquitous in numerous brain pathologies. A complete understanding of pathological conditions as well as normal brain function, therefore, hinges on elucidating the molecular and cellular pathways involved in these mostly interdependent variations. In this paper, we develop the first computational framework that combines the Hodgkin-Huxley type spiking dynamics, dynamic ion concentrations and glutamate homeostasis, neuronal and astroglial volume changes, and ion exchange with vasculature into a comprehensive model to elucidate the role of glutamate uptake in the dynamics of spreading depolarization (SD)-the electrophysiological event underlying numerous pathologies including migraine, ischemic stroke, aneurysmal subarachnoid hemorrhage, intracerebral hematoma, and trauma. We are particularly interested in investigating the role of glutamate in the duration and termination of SD caused by K+ perfusion and oxygen-glucose deprivation. Our results demonstrate that glutamate signaling plays a key role in the dynamics of SD, and that impaired glutamate uptake leads to recovery failure of neurons from SD. We confirm predictions from our model experimentally by showing that inhibiting astrocytic glutamate uptake using TFB-TBOA nearly quadruples the duration of SD in layers 2-3 of visual cortical slices from juvenile rats. The model equations are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles or a combination of these principles and known physiological facts. Accordingly, we claim that our approach can be used as a future guide to investigate the role of glutamate, ion concentrations, and dynamics cell volume in other brain pathologies and normal brain function.

Implementation of dynamic dual input multiple output logic gate via resonance in globally coupled Duffing oscillators

We have used a system of globally coupled double-well Duffing oscillators under an enhanced resonance condition to design and implement Dual Input Multiple Output (DIMO) logic gates. In order to enhance the resonance, the first oscillator in the globally coupled system alone is excited by two forces out of which one acts as a driving force and the other will be either sub-harmonic or super-harmonic in nature. We report that for an appropriate coupling strength, the second force coherently drives and enhances not only the amplitude of the weak first force to all the coupled systems but also drives and propagates the digital signals if any given to the first system. We then numerically confirm the propagation of any digital signal or square wave without any attenuation under an enhanced resonance condition for an amplitude greater than a threshold value. Further, we extend this idea for computing various logical operations and succeed in designing theoretically DIMO logic gates such as AND/NAND, OR/NOR gates with globally coupled systems.

A wind-powered one-way bistable medium with parity effects

We describe the design, construction, and dynamics of low-cost mechanical arrays of 3D-printed bistable elements whose shapes interact with wind to couple them one-way. Unlike earlier hydromechanical unidirectional arrays, our aeromechanical one-way arrays are simpler, easier to study, and exhibit a broader range of phenomena. Solitary waves or solitons propagate in one direction at speeds proportional to wind speeds. Periodic boundaries enable solitons to annihilate in pairs in arrays with an even number of elements. Solitons propagate indefinitely in odd arrays that frustrate pairing. Large noise spontaneously creates soliton-antisoliton pairs. Soliton annihilation times increase quadratically with initial separations, as expected for random-walk models of soliton collisions.

Anions Govern Cell Volume: A Case Study of Relative Astrocytic and Neuronal Swelling in Spreading Depolarization

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little about the dynamics of cell and tissue swelling, and the differential changes in the volumes of neurons and glia during pathological states such as spreading depolarizations (SD) under ischemic and non–ischemic conditions, and epileptic seizures. By combining the Hodgkin–Huxley type spiking dynamics, dynamic ion concentrations, and simultaneous neuronal and astroglial volume changes into a comprehensive model, we elucidate why glial cells swell more than neurons in SD and the special case of anoxic depolarization (AD), and explore the relative contributions of the two cell types to tissue swelling. Our results demonstrate that anion channels, particularly Cl⁻, are intrinsically connected to cell swelling and blocking these currents prevents changes in cell volume. The model is based on a simple and physiologically realistic description. We introduce model extensions that are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles, or by a phenomenological combination of these principles and known physiological facts. This work provides insights into numerous studies related to neuronal and glial volume changes in SD that otherwise seem contradictory, and is broadly applicable to swelling in other cell types and conditions.

Noise-induced suppression of nonlinear distortions in a bistable system with biharmonic excitation in vibrational resonance

This paper is a report of the experimental evidence of suppression of vibrational higher-order harmonics in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies in the phenomenon of vibrational resonance when an optimal amount of white, Gaussian noise is applied. A quantitative characterization of the suppression is given on the basis of the coefficient of nonlinear distortions. The behavior of the coefficient of nonlinear distortions is studied in wide ranges of the added noise intensity, the dc current, and the amplitude of the harmonic signals. The experimental results are compared with a numerical simulation of a Langevin model showing good agreement.

Resonance induced by a spatially periodic force in the reaction-diffusion system

The stimulus-dynamic response is an important topic in physics. In this work, we study the dynamics in the reaction-diffusion system subjected to a weak signal and a spatially periodic force. We find that the response of the system to the weak signal is enhanced largely by the spatially periodic force, which is termed spatially periodic-force-induced resonance. In particular, the response becomes stronger when the spatial frequency is chosen such that the system synchronizes with spatially periodic force. This combinative behavior, i.e., the spatially periodic-force-induced resonance and the spatial-synchronization-enhanced resonance, is of great interest and may shed light on our understanding of the dynamics of nonlinear systems subjected to spatially periodic force in responding to a weak signal.

Enhanced multiple vibrational resonances by Na+ and K+ dynamics in a neuron model

Some neuronal receptors perceive external input in the form of hybrid periodic signals. The signal detection may be based on the mechanism of vibrational resonance, in which a system's response to the low frequency signal can become optimal by an appropriate choice of the vibration amplitude of HFS. The vibrational resonance effect is investigated in a neuron model in which the intra- and extra-cellular potassium and sodium concentrations are allowed to evolve temporally, depending on ion currents, Na⁺-K⁺ pumps, glial buffering, and ion diffusion. Our results reveal that, compared to the vibrational resonances in the model with constant ion concentrations, the significantly enhanced vibrational multi-resonances can be observed for the single neuron system where the potassium and sodium ion concentrations vary temporally. Thus, in contradiction to a popular view that ion concentrations dynamics play little role in signal detection, we indicate that the neuron's response to an external subthreshold signal can be largely improved by sodium and potassium dynamics.

Experimental evidence of vibrational resonance in a multistable system

Experimental evidence of vibrational resonance in a multistable vertical-cavity surface-emitting laser (VCSEL) is reported. The VCSEL is characterized by a coexistence of four polarization states and driven by low-frequency (LF) and high-frequency (HF) periodic signals. In these conditions a series of resonances on the low frequency depending on the HF amplitude is observed. The location of resonances in a parameter space (dc current, amplitude of HF signal) is experimentally studied. For a fixed value of the dc current an evolution of the resonance curves with an increase of the LF amplitude is experimentally investigated.

Theoretical analysis of vibrational resonance in a neuron model near a bifurcation point

The FitzHugh-Nagumo neuron model subject to a biharmonical external force with two different frequencies is used to investigate the underlying mechanism of vibrational resonance in an excitable system in which the time scales between the fast and slow variables are separated clearly. The theoretical analysis is given based on the approximation approach and the concept of the phase-locking ratio instead of the amplification ratio widely used in the investigation of vibrational resonance in bistable oscillators. The result shows that the high-frequency subthreshold force with the frequency close to the natural frequency of the neuron model in the resting state can induce the change of potential shape of the model near the bifurcation point. This gives rise to the different phase-locking modes of the neuron responses to the same low-frequency subthreshold input. It is also shown that besides the parameters of the high-frequency force such as amplitude and frequency, the bifurcation parameter of the model can affect the vibrational resonance notably. Finally, the numerical results have verified the theoretical analysis.

Signal transmission in a Y-shaped one-way chain

It has been found that noise plays a key role to improve signal transmission in a one-way chain of bistable systems [Zhang et al., Phys. Rev. E 58, 2952 (1998)]. We here show that the signal transmission can be sharply improved without the aid of noise, if the one-way chain with a single source node is changed with two source nodes becoming a Y-shaped one-way chain. We further reveal that the enhanced signal transmission in the Y-shaped one-way chain is regulated by coupling strength, and that it is robust to noise perturbation and input signal irregularity. We finally analyze the mechanism of the enhanced signal transmission by the Y-shaped structure.

Effect of multiple time-delay on vibrational resonance

We report our investigation on the effect of multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a low- and a high-frequency periodic force. For the single oscillator, we obtain analytical expressions for the response amplitude Q and the amplitude g of the high-frequency force at which resonance occurs. The regions in parameter space of enhanced Q at resonance, as compared to the case in absence of time-delay, show a bands-like structure. For the two-coupled oscillators, we explain all the features of variation of Q with the control parameter g. For the system of n-coupled oscillators with a single time-delay coupling, the response amplitudes of the oscillators are shown to be independent of the time-delay. In the case of a multi time-delayed coupling, undamped signal propagation takes place for coupling strength (δ) above a certain critical value (denoted as δu). Moreover, the response amplitude approaches a limiting value QL with the oscillator number i. We obtain analytical expressions for both δu and QL.

Absolute negative mobility in a vibrational motor

An anomalous transport phenomenon termed absolute negative mobility (ANM) was observed in a vibrational motor, where an additional time-periodic signal filled the role usually played by noise in a Brownian motor. Within a tailored parameter regime, the ANM behavior is maximized at two regimes upon variation of the bias. The observed ANM still survives at a wide range of the driving strength and angular frequency of the additional signal.

Enhancement and weakening of stochastic resonance for a coupled system

In the paper, we investigate the phenomenon of stochastic resonance of a system with finite locally coupled linear elements driven by multiplicative dichotomous noise and temporal periodic signal. It is shown that, for some suitably selected values of the parameters, with increasing the size of the system or the coupling among the nearest elements, the stochastic resonance phenomenon can be enhanced; while for some other suitably selected parameters' values, with the increase of the size or the coupling, the phenomenon of stochastic resonance can be weakened. Our results can provide some useful insights for the investigation of the stochastic resonance phenomenon of the systems with locally (or globally) coupled finite (or infinite) elements.

Novel vibrational resonance in multistable systems

We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.

Frequency-resonance-enhanced vibrational resonance in bistable systems

The dynamics in an overdamped bistable system subject to the action of two periodic forces (assuming their frequencies are ω and Ω, and amplitudes are A and B, respectively) is studied. For the usual vibrational resonance, the nonmonotonic dependence of signal output of the low frequency ω on the change of B for a fixed Ω, the condition Ω≫ω is always assumed in all previous studies. Here, removing this restriction, we find that a resonant behavior can extensively occur with respect to the changes of both the frequency Ω and amplitude B. Especially, the resonance becomes stronger when Ω is chosen such that it is exactly in frequency resonance with ω. This combinative behavior, called frequency-resonance-enhanced vibrational resonance, is of great interest and may shed an improved light on our understanding of the dynamics of nonlinear systems subject to a biharmonic force.