Vibrational resonance induced by transition of phase-locking modes in excitable systems

Crisis-induced vibrational resonance in a phase-modulated periodic structure

Double vibrational resonance is reported for a driven oscillator in a periodic structure of the Josephson junction type with high-frequency phase modulation. We identify two distinct phase modulation effects, namely, resonant induction and resonant amplification, leading to the appearance of a double resonance. We analyze these vibrational resonance phenomena theoretically and numerically, and we show that the origin of the induced resonance is traceable to a transition from periodicity to quasiperiodicity associated with an attractor-merging crisis.

Energy dependence of synchronization mode transitions in the delay-coupled FitzHugh-Nagumo system driven by chaotic activity

Energy absorption and consumption are essential for the activity of single neurons and neuronal networks. The synchronization mode transition and energy dependence in a delay-coupled FitzHugh-Nagumo (FHN) neuronal system driven by chaotic activity are investigated in this paper. With the change of chaotic current intensity, it was found that the synchronization mode of coupled neurons undergoes synchronous state, transition state, anti-phase state, alternating asynchronous and anti-phase state, and chaotic current-induced chaotic state. The Hamiltonian energy is much dependent on the synchronization mode of coupled neurons. The synchronization mode and the Hamiltonian energy of coupled neurons can be modulated by chaotic current intensity, coupling strength and time delay. The introduction of the time delay induces the system to become bistable state. Chaotic current as an external force induced transitions between the synchronous and anti-phase states. Coupling strength is an intrinsic property of the system and can change the properties of the bistable state. Furthermore, the synchronous and anti-phase states appear intermittently with the increasing of time delay. A chained neuronal network is used to prove that the synchronization mode transition of the system of multiple neurons is similar to the two neurons. The results of this paper might help one to understand the intrinsic energy alteration mechanisms of neuronal synchronization.

Harnessing vibrational resonance to identify and enhance input signals

We report the occurrence of vibrational resonance and the underlying mechanism in a simple piecewise linear electronic circuit, namely, the Murali-Lakshmanan-Chua circuit, driven by an additional biharmonic signal with widely different frequencies. When the amplitude of the high-frequency force is tuned, the resultant vibrational resonance is used to detect the low-frequency signal and also to enhance it into a high-frequency signal. Further, we also show that even when the low-frequency signal is changed from sine wave to square and sawtooth waves, vibrational resonance can be used to detect and enhance them into high-frequency signals. These behaviors, confirmed by experimental results, are illustrated with appropriate analytical and numerical solutions of the corresponding circuit equations describing the system. Finally, we also verify the signal detection in the above circuit even with the addition of noise.

Improvement of signal propagation in the optoelectronic artificial spiking neuron by vibrational resonance

Experimental evidence of vibrational resonance (VR) in the optoelectronic artificial spiking neuron based on a single photon avalanche diode and a vertical cavity laser driven by two periodic signals with low and high frequencies is reported. It is shown that a very weak subthreshold low-frequency (LF) periodic signal can be greatly amplified by the additional high-frequency (HF) signal. The phenomenon shows up as a nonmonotonic resonant dependence of the LF response on the amplitude of the HF signal. Simultaneously, a strong resonant rise of the signal-to-noise ratio is also observed. In addition, for the characterization of VR an area under the first LF period in the probability density function of interspike intervals for the LF signal and the maximal amplitude in this area were used, both of which also demonstrate a resonant behavior depending on the amplitude of the HF signal.

Coexisting Firing Patterns in an Improved Memristive Hindmarsh-Rose Neuron Model with Multi-Frequency Alternating Current Injection

With the development of memristor theory, the application of memristor in the field of the nervous system has achieved remarkable results and has bright development prospects. Flux-controlled memristor can be used to describe the magnetic induction effect of the neuron. Based on the Hindmarsh-Rose (HR) neuron model, a new HR neuron model is proposed by introducing a flux-controlled memristor and a multi-frequency excitation with high-low frequency current superimposed. Various firing patterns under single and multiple stimuli are investigated. The model can exhibit different coexisting firing patterns. In addition, when the memristor coupling strength changes, the multiple stability of the model is eliminated, which is a rare phenomenon. Moreover, an analog circuit is built to verify the numerical simulation results.

Effects of chaotic activity and time delay on signal transmission in FitzHugh-Nagumo neuronal system

The influences of chaotic activity and time delay on the transmission of the sub-threshold signal (STS) in a single FitzHugh-Nagumo neuron and coupled neuronal networks are studied. It is found that a moderate chaotic activity level can enhance the system's detection and transmission of STS. This phenomenon is known as chaotic resonance (CR). In a single neuron, the large amplitude and small period of the STS have a positive effect on the CR phenomenon. In the coupled neuronal network, however, the signal transmission performance of chemical synapses is better than that of electrical synapses. The time delay can determine the trend of the system response, and the multiple chaotic resonances phenomenon is observed upon fine-tuning the time delay length. Both sub-harmonic chaotic resonance and chaotic anti-resonance appear when the STS period and time delay are locked. In chained networks, the signal transmission performance between electrical synapses attenuates continuously. Conversely, the performance between chemical synapses reaches a steady state.

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)'.

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.

Ionic channel blockage in stochastic Hodgkin-Huxley neuronal model driven by multiple oscillatory signals

Ionic channel blockage and multiple oscillatory signals play an important role in the dynamical response of pulse sequences. The effects of ionic channel blockage and ionic channel noise on the discharge behaviors are studied in Hodgkin-Huxley neuronal model with multiple oscillatory signals. It is found that bifurcation points of spontaneous discharge are altered through tuning the amplitude of multiple oscillatory signals, and the discharge cycle is changed by increasing the frequency of multiple oscillatory signals. The effects of ionic channel blockage on neural discharge behaviors indicate that the neural excitability can be suppressed by the sodium channel blockage, however, the neural excitability can be reversed by the potassium channel blockage. There is an optimal blockage ratio of potassium channel at which the electrical activity is the most regular, while the order of neural spike is disrupted by the sodium channel blockage. In addition, the frequency of spike discharge is accelerated by increasing the ionic channel noise, the firing of neuron becomes more stable if the ionic channel noise is appropriately reduced. Our results might provide new insights into the effects of ionic channel blockages, multiple oscillatory signals, and ionic channel noises on neural discharge behaviors.

Effect of external periodic signals and electromagnetic radiation on autaptic regulation of neuronal firing

An improved Hindmarsh-Rose (HR) neuron model, where the memristor is a bridge between membrane potential and magnetic flux, can be used to investigate the effect of periodic signals on autaptic regulation of neurons under electromagnetic radiation. Based on the improved HR model driven by periodic high-low-frequency current and electromagnetic radiation, the responses of electrical autaptic regulation with diverse high-low-frequency signals are investigated using bifurcation analysis. It is found that the electrical modes of neurons are determined by the selecting parameters of both periodic high and low-frequency current and electromagnetic radiation, and the Hamiltonian energy depends on the neuronal firing modes. The effects of Gaussian white noise on the membrane potential are discussed using numerical simulations. It is demonstrated that external high-low-frequency stimulus plays a significant role in the autaptic regulation of neural firing mode, and the electrical mode of neurons can be affected by the angular frequency of both high-low-frequency forcing current and electromagnetic radiation. The mechanism of neuronal firing regulated by high-low-frequency signal and electromagnetic radiation discussed here could be applied to research neuronal networks and synchronisation modes.

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.

Subthreshold and suprathreshold vibrational resonance in the FitzHugh-Nagumo neuron model

We study the subthreshold and suprathreshold vibrational resonance in the FitzHugh-Nagumo neuron model. For the subthreshold situation, two cases where the stationary states are equilibrium point and limit cycle are considered, where different natures of vibrational resonance are observed via theoretical and numerical methods. Especially when the frequency of the high-frequency driving force is near the so-called canard-resonance frequency, the firing rate can be significantly enhanced at the presence of noise. For the suprathreshold situation, we show that the local maxima of the response amplitude are located at the transition boundaries of different phase-locking patterns. The minimal required forcing amplitudes of high-frequency signal of the firing onset are just multiples of the spiking frequency. Furthermore, phase portraits and time series show that the presence of the global maxima of the response results from not only the suprathreshold but also the subthreshold phase-locking modes. In spite of the distinct characteristics for two stationary states on subthreshold oscillation, the suprathreshold vibrational resonance showed no qualitative difference between the two cases.

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.

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.

Endogenous field feedback promotes the detectability for exogenous electric signal in the hybrid coupled population

This paper presents the endogenous electric field in chemical or electrical synaptic coupled networks, aiming to study the role of endogenous field feedback in the signal propagation in neural systems. It shows that the feedback of endogenous fields to network activities can reduce the required energy of the noise and enhance the transmission of input signals in hybrid coupled populations. As a common and important nonsynaptic interactive method among neurons, particularly, the endogenous filed feedback can not only promote the detectability of exogenous weak signal in hybrid coupled neural population but also enhance the robustness of the detectability against noise. Furthermore, with the increasing of field coupling strengths, the endogenous field feedback is conductive to the stochastic resonance by facilitating the transition of cluster activities from the no spiking to spiking regions. Distinct from synaptic coupling, the endogenous field feedback can play a role as internal driving force to boost the population activities, which is similar to the noise. Thus, it can help to transmit exogenous weak signals within the network in the absence of noise drive via the stochastic-like resonance.

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.

An ephaptic transmission model of CA3 pyramidal cells: an investigation into electric field effects

Extracellular electric fields existing throughout the living brain affect the neural coding and information processing via ephaptic transmission, independent of synapses. A two-compartment whole field effect model (WFEM) of pyramidal neurons embedded within a resistive array which simulates the extracellular medium i.e. ephapse is developed to study the effects of electric field on neuronal behaviors. We derive the two linearized filed effect models (LFEM-1 and LFEM-2) from WFEM at the stable resting state. Through matching these simplified models to the subthreshold membrane response in experiments of the resting pyramidal cells exposed to applied electric fields, we not only verify our proposed model's validity but also found the key parameters which dominate subthreshold frequency response characteristic. Moreover, we find and give its underlying biophysical mechanism that the unsymmetrical properties of active ion channels results in the very different low-frequency response of somatic and dendritic compartments. Following, WFEM is used to investigate both direct-current (DC) and alternating-current field effect on the neural firing patterns by bifurcation analyses. We present that DC electric field could modulate neuronal excitability, with the positive field improving the excitability, the modest negative field suppressing the excitability, but interestingly, the larger negative field re-exciting the neuron back into spiking behavior. The neuron exposed to the sinusoidal electric field exhibits abundant firing patterns sensitive to the input frequency and intensity. In addition, the electrical properties of ephapse can modulate the efficacy of field effect. Our simulated results are qualitatively in line with the relevant experimental results and can explain some experimental phenomena. Furthermore, they are helpful to provide the predictions which can be tested in future experiments.