Resonance Analyses for a Noisy Coupled Brusselator Model

We discuss the dynamical behavior of a chemical network arising from the coupling of two Brusselators established by the relationship between products and substrates. Our interest is to investigate the coherence resonance(CR)phenomena caused by noise for a coupled Brusselator model in the vicinity of the Hopf bifurcation, which can be determined by the signal-to-noise ratio(SNR). The CR in two coupled Brusselators will be considered in the presence of the Gaussian colored noise and two uncorrelated Gaussian white noises. Simulation results show that,for the case of single noise, the SNR characterizing the degree of temporal regularity of coupled model reaches a maximum value at some optimal noise levels, and the noise intensity can enhance the CR phenomena of both subsystems with a similar trend but in different resonance degrees. Meanwhile, effects of noise intensities on CR of the second subsystem are opposite for the systems under two uncorrelated Gaussian white noises. Moreover,we find that CR might be a general phenomenon in coupled systems.     

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.     

Mean First-Passage Time of an Asymmetric Kinetic Model Driven by Two Different Kinds of Colored Noises

The mean first-passage time （MFPT） of an asymmetric bistable system between multiplicative non-Gaussian noise and additive Gaussian white noise with nonzero cross-correlation time is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker Planck equation is obtained by applying the unified colored noise approximation and the.Novikov Theorem. The steady-state probability distribution （SPD） is also obtained. The basal functional analysis and simplification are employed to obtain the approximate expressions of MFPT T^±. The effects of the asymmetry parameter β, the non-Gaussian parameter （measures deviation from Gaussian character） r, the noise correlation times τ and τ2, the coupling coefficient A, the intensities D and a of noise on the MFPT are discussed. It is found that the asymmetry parameter β, the non-Gaussian parameter r and the coupling coefficient A can induce phase transition. Moreover, the main findings are that the effect of self-existent parameters （D, α, and τ） of noise and cross-correlation parameters （A, 7-2） between noises on MFPT T^± is different.     

Correlated noise induced spatiotemporal coherence resonance in a square lattice network

The effects of additive correlated noise, which is composed of common Gaussian white noise and local Gaussian colored noise, on a square lattice network locally modelled by the Rulkov map are studied. We focus on the ability of noise to induce pattern formation in a resonant manner. It is shown that local Gaussian colored noise is able to induce pattern formation, which is more coherent at some noise intensity or correlation time, so it is able to induce spatiotemporal coherence resonance in the network. When common Gaussian white noise is applied in addition, it is seen that the correlated noise can induce coherent spatial structures at some intermediate noise correlation, while this is not the case for smaller and larger noise intensities. The mechanism of the observed spatiotemporal coherence resonance is discussed. It is also found that the correlation time of local colored noise has no evident effect on the optimal value of the noise strength for spatiotemporal coherence resonance in the network.     

Effects of Colored Noise on Periodic Orbits in a One-Dimensional Map

Noise can induce inverse period-doubling transition and chaos. The effects of the colored noise on periodic orbits, of the different periodic sequences in the logistic map, are investigated. It is found that the dynamical behaviors of the orbits, induced by an exponentially correlated colored noise, are different in the mergence of transition, and the effects of the noise intensity ontheir dynamical behaviors are different from the effects of the correlation time of noise. Remarkably, the noise can induce new periodic orbits, namely, two new orbits emerge in the period-four sequence at the bifurcation parameter value μ=3.5, four new orbits in the period-eight sequence at μ=3.55, and three new orbits in the period-six sequence at μ= 3.846, respectively.Moreover, the dynamical behaviors of the new orbits clearly show theresonance like response to the colored noise.     

Spiral Wave in Small-World Networks of Hodgkin--Huxley Neurons

The effect of small-world connection and noise on the formation and transitionof spiral wave in the networks of Hodgkin-Huxley neurons are investigated in detail. Some interesting results are found in our numerical studies. i) The quiescent neurons are activated to propagate electric signal to others by generating and developing spiral wave from spiral seed in small area. ii) A statistical factor is defined to describe the collective properties and phase transition induced by the topology of networks and noise. iii) Stable rotating spiral wave can be generated and keeps robust when the rewiring probability is below certain threshold, otherwise, spiral wave can not be developed from the spiral seed and spiral wave breakup occurs for a stable rotating spiral wave. iv) Gaussian white noise is introduced on the membrane of neuronsto study the noise-induced phase transition on spiral wave in small-world networks of neurons. It is confirmed that Gaussian white noise plays active role in supporting and developing spiral wave in the networks of neurons, and appearance of smaller factor of synchronization indicates high possibility to induce spiral wave.     

Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored. Unlike the existing work in detecting early warning signals, this paper presents the most probable transition paths to characterize the regime shifts. The most probable transition paths are obtained by minimizing the Freidlin-Wentzell (FW) action functional and Onsager-Machlup (OM) action functional, respectively. The most probable path shows the movement trend of the lake eutrophication system under noise excitation, and describes the global transition behavior of the system. Under the excitation of Gaussian noise, the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths. Under the excitation of Gaussian white noise and periodic force, we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.     

Noise-induced collective regimes of complex system in contact with a random reservoir

Based on a system-reservoir model, where the reservoir is driven by an external white Gaussian noise, we study the behavior of system components in Weiss mean-field approach and Gaussian approximation for moments. Crossover from individual to cooperative dynamics of the system components is due to noise. The system displays a transition similar to diversity-induced phase transition. The analytical results are compared with the numerical simulations.     

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.     

高斯白噪声对神经元二维映射模型动力学的影响

从神经元二维映射模型出发，用高斯白噪声模拟了神经元的噪声环境，进而研究了高斯白噪声对参数空间相图的影响.研究发现，噪声可以提高系统的可兴奋性.通过数值模拟研究了噪声引起的相干共振现象.结果表明，只有当系统参数选取在静息区域且接近连续点火和静息状态分界线时才可以得到相干共振现象. 关键词： 高斯白噪声 神经元二维映射模型 相图 相干共振     

Fractional Gaussian noise-induced evolution and transition in anti-tumor model

Noise induced evolution and transition in an anti-tumor model under immune surveillance are investigated in the presence of additive fractional Gaussian noises. Unlike white Gaussian noise, the Hurst exponent of noise plays a constructive role in the evolution. The noise can also induce the transition. As the noise intensity increases, the noises induced the transition from two states to one state for antipersistent case, whereas the curve always presents a bimodal structure and only the heights of their peaks changed for the persistent case.     

Noise-Induced Transition in a Voltage-Controlled Oscillator Neuron Model

In the presence of Gaussian white noise, we study the properties of voltage-controlled oscillator neuron model and discuss the effects of the additive and multiplicative noise. It is found that the additive noise can accelerate and counterwork the firing of neuron, which depends on the value of central frequency of neuron itself, while multiplicative noise can induce the continuous change or mutation of membrane potential.     

Dynamical Mean-Field Equations for a Neural Network with Spike Timing Dependent Plasticity

We study the discrete dynamics of a fully connected network of threshold elements interacting via dynamically evolving synapses displaying spike timing dependent plasticity. Dynamical mean-field equations, which become exact in the thermodynamical limit, are derived to study the behavior of the system driven with uncorrelated and correlated Gaussian noise input. We use correlated noise to verify that our model gives account to the fact that correlated noise provides stronger drive for synaptic modification. Further we find that stochastic independent input leads to a noise dependent transition to the coherent state where all neurons fire together, most notably there exists an optimal noise level for the enhancement of synaptic potentiation in our model.     

Frequency-selective response of FitzHugh-Nagumo neuron networks via changing random edges

We consider a network of FitzHugh-Nagumo neurons; each neuron is subjected to a subthreshold periodic signal and independent Gaussian white noise. The firing pattern of the mean field changes from an internal-scale dominant pattern to an external-scale dominant one when more and more edges are added into the network. We find numerically that (a) this transition is more sensitive to random edges than to regular edges, and (b) there is a saturation length for random edges beyond which the transition is no longer sharpened. The influence of network size is also investigated.     

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加.     

周期矩形信号作用下时滞非对称单稳系统 的随机共振

研究了周期矩形信号对时滞非对称单稳系统随机共振的影响,系统中加入的噪声均为Gauss白噪声.得到了信噪比的解析表达式,通过分析信噪比曲线发现系统存在随机共振现象.数值结果还表明乘性与加性噪声强度对信噪比的影响是不同的,在SNR-D参数平面上共振与抑制共存.在信噪比随着时滞量变化的曲线图上发现,当系统的非对称性|r|取值很大或者乘性与加性噪声强度比D/α小于1时,参数平面上的随机共振现象会消失.     

Two Stochastic Resonances Induced by Two Different Multiplicative Telegraphic Noises for an Electric System

In this paper, an electric system with two dichotomous resistors is investigated. It is shown that this system can display two stochastic resonances, which are the amplitude of the periodic response as the functions of the two dichotomous resistors strengthes respectively. In the limits of Gaussian white noise and shot white noise (i.e., the two noises are both Gaussian white noise or shot white noise), no phenomena of resonance appear. By further study, we find that when the system is with three or more multiplicative telegraphic noises, there are three or more stochastic resonances.     

Multiplicative non-Gaussian noise and additive Gaussian white noise induced transition in a piecewise nonlinear model

We study the transition problems in a piecewise nonlinear model induced by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Firstly, applying the path integral approach, the unified colored noise approximation, the analytical expression of the steady-state probability density function (SPD) is derived. Then the change regulation of the SPD is analyzed with the change of the strength and relevance of multiplicative noise and additive noise. From numerical computations we obtain some new nonlinear phenomena: the transition can be induced by the cross-correlation strength between noises, the non-Gaussian noise intensity and the Gaussian noise intensity as well as the non-Gaussian noise deviation parameter. This indicates that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. Moreover, we also find the correlation time of the non-Gaussian noise can not induce the transition.     

Fluctuation of Parameters in Tumor Cell Growth Model

We study the steady state properties of a logistic growth model in the presence of Gaussian white noise.Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution function and its extrema have been investigated. It is found that the fluctuation of the tumor birth rate reduces the population of the cells while the fluctuation of predation rate can prevent the population of tumor ceils from going into extinction.Noise in the system can induce the phase transition.     

Fluctuation of Parameters in Tumor Cell Growth Model

We study the steady state properties of a logistic growth model in the presence of Gaussian white noise.Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution functionand its extrema have been investigated. It is found that the fluctuation of the tumor birth rate reduces the populationof the cells while the fluctuation of predation rate can prevent the population of tumor cells from going into extinction.Noise in the system can induce the phase transition.