Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.     

Noise-induced coherence in an excitable system

Noise-induced coherence resonance, an effect akin to the well-known phenomenon of stochastic resonance, has been described recently for excitable systems driven by white noise. The purpose of this Letter is to show that coherence enhancement in a system of this kind can also be achieved by modifying the correlation time of the noise.     

Experimental deterministic coherence resonance

We demonstrate coherence resonance in a dynamical system without external noise. The experimental evidence is reported in the low frequency fluctuations of a chaotic diode laser with optical feedback. The phenomenon is also verified numerically using the Lang-Kobayashi equations for a single solitary mode laser, without noise terms. Fast deterministic dynamics plays the role of an effective exciting noise, narrowing the resonance in the autonomous slow power drop cycles of the laser. This new result is the natural extension of deterministic stochastic resonance and noise induced coherence resonance predicted and observed in recent years.     

Effects of noise on excitable dissipative solitons

We study the effects of noise on excitable DS found on nonlinear Kerr cavities, showing that the system exhibits coherence resonance, characterized by a maximum degree of regularity for intermediate noise intensities. This behavior is observed for two different ways of applying noise: an additive white uncorrelated spatio-temporal noise and including fluctuations in the intensity of an addressing beam.     

Coherence resonance in coupled chaotic oscillators

Existing works on coherence resonance, i.e., the phenomenon of noise-enhanced temporal regularity, focus on excitable dynamical systems such as those described by the FitzHugh-Nagumo equations. We extend the scope of coherence resonance to an important class of dynamical systems: coupled chaotic oscillators. In particular, we show that, when a system of coupled chaotic oscillators is under the influence of noise, the degree of temporal regularity of dynamical variables characterizing the difference among the oscillators can increase and reach a maximum value at some optimal noise level. We present numerical results illustrating the phenomenon and give a physical theory to explain it.     

Noise-induced front motion: signature of a global bifurcation

We show that front motion can be induced by noise in a spatially extended excitable system with a global constraint. Our model system is a semiconductor superlattice exhibiting complex dynamics of electron accumulation and depletion fronts. The presence of noise induces a global change in the dynamics of the system forcing stationary fronts to move through the entire device. We demonstrate the effect of coherence resonance in our model; i.e., there is an optimal level of noise at which the regularity of front motion is enhanced. Physical insight is provided by relating the space-time dynamics of the fronts with a phase-space analysis.     

Experimental evidence of coexisting periodic stochastic resonance and coherence resonance phenomena

We report evidence of coexisting period stochastic resonance (PSR) and coherence resonance (CR) phenomena in an electrochemical cell. The anodic voltage (V) in the cell is chosen such that the anodic current (I) exhibits excitable fixed point behavior. Subsequently, the anodic voltage is modulated by an external perturbation that is a composite of a subthreshold periodic pulse signal and Gaussian white noise (GWN). As the amplitude of the GWN is increased, the regularity of the invoked dynamics is analyzed using normalized variance curve. The calculated resonance curve shows a double minima, implying the existence of two optimum noise levels where enhanced regularity of the induced spike sequence is detected. Numerical simulations corroborate experimental findings.     

Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation

We analyze noise-induced phenomena in nonlinear dynamical systems near a subcritical Hopf bifurcation. We investigate qualitative changes of probability distributions (stochastic bifurcations), coherence resonance, and stochastic synchronization. These effects are studied in dynamical systems for which a subcritical Hopf bifurcation occurs. We perform analytical calculations, numerical simulations and experiments on an electronic circuit. For the generalized Van der Pol model we uncover the similarities between the behavior of a self-sustained oscillator characterized by a subcritical Hopf bifurcation and an excitable system. The analogy is manifested through coherence resonance and stochastic synchronization. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with hard excitation, can be partially synchronized even outside the oscillatory regime of the deterministic system.     

Influence of Coupling Delay on Noise Induced Coherent Oscillations in Excitable Systems

Influence of small time-delays in coupling between noisy excitable systems on the coherence resonance and self-induced stochastic resonance is studied. Parameters of delayed coupled deterministic excitable units are chosen such that the system has only one attractor, namely the stationary state, for any value of the coupling and the time-lag. Addition of white noise induces qualitatively different types of coherent oscillations, and we analyzed the influence of coupling time-delay on the properties of these coherent oscillations. The main conclusion is that time-lag τ≥1, but still smaller than the refractory period, and sufficiently strong coupling drastically change signal to noise ratio in the quantitative and qualitative way. An interval of noise values implies quite large signal to noise ratio and different types of noise induced coherence are greatly enhanced. We also observed coincident spiking for small noise intensity and time-lag proportional to the inter-spike interval of the coherent spike trains. On the other hand, time-lags τ<1 and/or weak coupling induce negligible changes in the properties of the stochastic coherence.     

From Autonomous Coherence Resonance to Periodically Driven Stochastic Resonance

In periodically driven nonlinear stochastic systems, noise may play a role of enhancing the output periodic signal （termed as stochastic resonance or SR）. While in autonomous excitable systems, noise may play a role of increasing coherent motion （termed as coherence resonance or CR）. So far the topics of SR and CR have been investigated separately as two major fields of studying the active roles of noise in nonlinear systems. We find that these two topics are closely related to each other. Specifically, SR occurs in such periodically driven systems that the corresponding autonomous systems show CR. The SR with sensitive frequency dependence can be observed when the corresponding autonomous system shows CR with finite characteristic frequency. Moreover, ‘resonant noise＇ and ‘resonant frequency＇ of SR coincide with those of CR.     

Noise induced amplification of sub-threshold pulses in multi-thread excitable semiconductor ‘neurons’

We report on the transmission of electrical pulses through a semiconductor structure which emulates biological neurons. The ‘neuron’ emits bursts of electrical spikes whose coherence we study as a function of the amplitude and frequency of a sine wave stimulus and noise. Noise is found to enhance the transmission of pulses below the firing threshold of the neuron. We demonstrate stochastic resonance when the power of the output signal passes through a maximum at an optimum noise value. Under appropriate conditions, we observe coherence resonance and stochastic synchronization. Data are quantitatively explained by modelling the FitzHugh–Nagumo equations derived from the electrical equivalent circuit of the soma. We have therefore demonstrated a physically realistic neuron structure that provides first principles feedback on mathematical models and that is well suited to building arborescent networks of pulsing neurons.     

Experimental evidence of coherence resonance in a time-delayed bistable system

We report on the experimental observation of coherence resonance in a bistable system with delay. Our system consists of a vertical-cavity surface-emitting laser subject to time-delayed optical feedback simultaneously from a long and from an extremely short external cavity. Coherence resonance is experimentally proven by analysis of the residence time distribution of the polarization mode-hopping regime and of the signal to noise ratio in the power spectrum.     

Firing rates of coupled noisy excitable elements

The dynamics of coupled excitable FitzHugh Nagumo systems under external noisy driving is studied. Different from most of previous work focusing on the noise-induced regularity in the framework of coherence resonance, here the average frequency （or firing rate） of coupled excitable elements is of much more concern. We find that （i） their frequencies first increase and then decrease with the increase of the coupling, and there is a clear crossover from a rush increase to a smooth increase with the increase of noise strength, and （ii） for nonidentical cases, all elements transit to an identical frequency simultaneously only after a certain coupling strength is achieved. These first-increase-thendecrease non-monotonic frequency behavior and isochronous frequency synchronization are believed to be two basic behaviors in coupled noisy excitable systems.     

白噪声诱发Morris-Lecar模型构成的Ⅱ型兴奋网络产生多次空间相干共振

为研究噪声在网络中的作用及对时空行为的影响, 通过电耦合、近邻连接的Morris-Lecar模型构建了同质可兴奋细胞网络. 单元振子的确定性行为表现为Ⅱ型兴奋性的静息. 在高斯白噪声的作用下, 网络会在较大的噪声强度范围产生螺旋波, 以及在某些较小的噪声强度范围产生杂乱的空间结构. 随着噪声强度的增加, 螺旋波的结构会在简单和复杂之间转换, 或与杂乱的空间结构交替出现. 通过空间结构函数及其信噪比的计算, 发现简单螺旋波的信噪比较大, 复杂螺旋波以及杂乱的时空结构的信噪比较小. 信噪比随着噪声强度的增加会出现多次极大值, 说明白噪声可以在可兴奋细胞网络中诱导多次空间相干共振. 研究结果提示现实的可兴奋系统能有多次机会选择不同强度的噪声加以合理利用.     

Delayed feedback as a means of control of noise-induced motion

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.     

Topologically inequivalent orbits induced by noise

In this Letter we extend the concept of stochastic resonance. We show that in forced excitable systems noise can be responsible for the appearance of recurrences presenting a robust topological organization inequivalent to the periodic orbits of the deterministic system. As in stochastic resonance, these new structures are most pronounced at an optimal noise intensity.     

Excitability in a semiconductor laser with saturable absorber

We show that a monolithic and compact vertical cavity laser with intracavity saturable absorber can emit short excitable pulses. These calibrated optical pulses can be excited as a response to an input perturbation whose amplitude is above a certain threshold. Subnanosecond excitable response is promising for applications to novel all-optical devices for information processing or logical gates.     

Optical and photocurrent spectroscopy with picosecond strain pulses

This paper gives an overview of optical experiments using picosecond strain pulses. The strain pulses, which propagate with the sound velocity, are incident on a semiconductor nanostructure and induce an ultrafast shift of the exciton resonance energy by an amount, that exceeds the spectral width of the corresponding optical transition. When the duration of the high-amplitude strain pulse is long enough compared with the coherence time of the optical resonance, modulation of the resonance takes place adiabatically and exciton energy can be accurately defined at each momentary position. If the coherence time exceeds the characteristic time of the strain pulse, a non-adiabatic regime is realized and the exciton cannot be related to an optical transition with a specific photon energy. In more detail, we describe the recent experiments on the gating of photocurrent in a tunneling p-i-n device and the generation of THz polariton sidebands in an optical microcavity strongly coupled to the excitons in an embedded quantum well. These two experiments represent, respectively, examples of adiabatic and non-adiabatic behaivior of excitons in the presence of the high-amplitude picosecond strain pulse.     

Coherence resonance in an excitable potential well

The excitable behaviour is considered as motion of a particle in a potential field in the presence of dissipation. The dynamics of the oscillator proposed in the present paper corresponds to the excitable behaviour in a potential well under condition of positive dissipation. Type-II excitability of the offered system results from intrinsic peculiarities of the potential well, whose shape depends on a system state. Concept of an excitable potential well is introduced. The effect of coherence resonance and self-oscillation excitation in a state-dependent potential well under condition of positive dissipation are explored in numerical experiments.     

Phase synchronization in coupled nonidentical excitable systems and array-enhanced coherence resonance

We study the dynamics of a lattice of coupled nonidentical Fitz Hugh-Nagumo system subject to independent external noise. It is shown that these stochastic oscillators can lead to global synchronization behavior without an external signal. With the increase of the noise intensity, the system exhibits coherence resonance behavior. Coupling can enhance greatly the noise-induced coherence in the system.