Stochastic Signal Induced Multiple Spatial Coherence Resonances and Spiral Waves in Excitable Media

Multiple spatial coherence resonances and spiral waves with various temporal-spatial structures are simulated in a two-dimensional network of excitable cells driven by a stochastic signal. The relationship between the multiple resonances and correspondingly different transitions of the spiral wave are elucidated. The results further provide a possible approach of applications of stochastic signal to evoke pattern transitions in excitable media.     

Noise-induced switching in two adaptively coupled excitable systems

We demonstrate that the interplay of noise and plasticity gives rise to slow stochastic fluctuations in a system of two adaptively coupled active rotators with excitable local dynamics. Depending on the adaptation rate, two qualitatively different types of switching behavior are observed. For slower adaptation, one finds alternation between two modes of noise-induced oscillations, whereby the modes are distinguished by the different order of spiking between the units. In case of faster adaptation, the system switches between the metastable states derived from coexisting attractors of the corresponding deterministic system, whereby the phases exhibit a bursting-like behavior. The qualitative features of the switching dynamics are analyzed within the framework of fast-slow analysis.     

随机共振系统输入阈值的频率特性

通过对双稳态系统和Ｈｉｎｄｍａｒｓｈ-Ｒｏｓｅ神经元输入信号阈值的频率特性进行数值计算，分别研究了非自激和可自激随机共振系统输入阈值随信号频率的依赖关系，提出了确定非自激系统阈值的频率特性的解析方法；指出了可自激系统阈值的频率特性可能在某些频区出现反常极小现象，并对产生这一现象的物理原因进行了理论分析． 关键词：     

Chaotically spiking canards in an excitable system with 2D inertial fast manifolds

We introduce a new class of excitable systems with two-dimensional fast dynamics that includes inertia. A novel transition from excitability to relaxation oscillations is discovered where the usual Hopf bifurcation is followed by a cascade of period doubled and chaotic small excitable attractors and, as they grow, by a new type of canard explosion where a small chaotic background erratically but deterministically triggers excitable spikes. This scenario is also found in a model for a nonlinear Fabry-Perot cavity with one pendular mirror.     

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.     

Dynamics of critical Kauffman networks under asynchronous stochastic update

We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is in strong contrast to the synchronous case, where the number of attractors grows faster than any power law.     

Chaotic wave trains in an oscillatory/excitable medium

We study the chaotic dynamics of a heterogeneous reaction–diffusion medium composed of two uniform regions: one oscillatory, and the other excitable. It is shown that, by altering the diffusion coefficient, local chaotic oscillations can be induced at the interface between regions, which in turn, generate different chaotic sequences of pulses traveling in the excitable region. We analyze the properties of the local chaotic driver, as well as the diffusion-induced transitions. A procedure based on the abnormal frequency-locking phenomenon is proposed for controlling such sequences. Relevance of the obtained results to cardiac dynamics is briefly discussed.     

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.     

Excitability of periodic and chaotic attractors in semiconductor lasers with optoelectronic feedback

The dynamics of a semiconductor laser with AC-coupled nonlinear optoelectronic feedback has been experimentally studied. A period doubling sequence of small periodic and chaotic attractors is observed, each of them displaying excitable features. This scenario is found also in a simplified physical model of the system, thus extending the concept of excitability, usually associated to fixed points, also to the case of higher-dimensional attractors.     

非线性动力系统分岔点邻域内随机共振的特性

研究了叉形分岔系统和FitzHugh Nagumo(FHN)细胞模型两种非线性动力系统分岔点邻域内 随机共振的特性.研究结果表明：这两种系统在分岔发生时具有由一个吸引子变为两个吸引 子或者由两个吸引子变为一个吸引子共同的分岔特性，即在分岔点的邻域内, 系统在分岔点 的两侧有分岔前吸引子和分岔后吸引子存在，在噪声的作用下，系统的运动除了像传统随机 共振的机理那样在分岔点一侧共存的吸引子之间跃迁，还在分岔点两侧三个吸引子（分岔前 一个吸引子和分岔后两个吸引子）之间跃迁，并且这种跃迁单独诱发了随机共振 ；在两种 跃迁都发生的情况下, 在其分岔点的邻域内，由第二种跃迁诱发的随机共振在引起第一种跃 迁噪声的强度很大的范围内变化仍可维持, 而第一种跃迁诱发的随机共振在引起第二种跃迁 噪声的强度很小的范围内变化即迅速消失. 关键词： 随机共振 吸引子 分岔点 跃迁     

忆阻器混沌电路产生的共存吸引子与Hopf分岔

利用荷控忆阻器和一个电感串联设计一种新型浮地忆阻混沌电路.用常规动力学分析方法研究该系统的基本动力学特性,发现系统可以产生一对关于原点对称的"心"型吸引子.将观察混沌吸引子时关注的电压、电流推广到功率和能量信号,观察到蝴蝶结型奇怪吸引子的产生.理论分析Hopf分岔行为并通过数值仿真进行验证,结果表明系统随电路参数变化能产生Hopf分岔、反倍周期分岔两种分岔行为.相对于其它忆阻混沌电路该电路采用的是一个浮地型忆阻器,并且在初始状态改变时,能产生共存吸引子和混沌吸引子与周期极限环共存现象.     

随机相位扰动抑制激发介质中漂移的螺旋波

研究了一类二维变量描述的激发系统中漂移螺旋波的抑制问题.通过在整个系统中局部注入带随机相位的电信号，如在系统256×256格点的边界或中心区域中选取4×4或者5×5格点区域施加一个带随机相位的外部激励电信号，在系统内部产生一个持续的靶波信号，实现靶波对螺旋波的动态竞争.数值计算表明：该方法对于Barkley模型中螺旋波有很强的抑制作用，与简单的局部周期信号驱动比较，具有暂态过程比较短的特点，而且对于时空噪声具有一定的抗干扰性.在一定的噪声范围内，即使系统出现不均匀性，也可以观测到靶波，新出现的靶波对螺旋波有抑制作用. 关键词： 螺旋波 靶波 Barkley模型 随机相位     

Noise-induced synchronous stochastic oscillations in small scale cultured heart-cell networks

This paper reports that the synchronous integer multiple oscillations of heart-cell networks or clusters are observed in the biology experiment.The behaviour of the integer multiple rhythm is a transition between super-and subthreshold oscillations,the stochastic mechanism of the transition is identified.The similar synchronized oscillations are theoretically reproduced in the stochastic network composed of heterogeneous cells whose behaviours are chosen as excitable or oscillatory states near a Hopf bifurcation point.The parameter regions of coupling strength and noise density that the complex oscillatory rhythms can be simulated are identified.The results show that the rhythm results from a simple stochastic alternating process between super-and sub-threshold oscillations.Studies on single heart cells forming these clusters reveal excitable or oscillatory state nearby a Hopf bifurcation point underpinning the stochastic alternation.In discussion,the results are related to some abnormal heartbeat rhythms such as the sinus arrest.     

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.     

Attractive target wave patterns in complex networks consisting of excitable nodes

This review describes the investigations of oscillatory complex networks consisting of excitable nodes,focusing on the target wave patterns or say the target wave attractors.A method of dominant phase advanced driving(DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations,such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks.The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns.Therefore,the center(say node A) and its driver(say node B) of a target wave can be used as a label,(A,B),of the given target pattern.The label can give a clue to conveniently retrieve,suppress,and control the target waves.Statistical investigations,both theoretically from the label analysis and numerically from direct simulations of network dynamics,show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large,and all these attractors can be labeled and easily controlled based on the information given by the labels.The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.     

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.     

Recurrence analysis of strange nonchaotic dynamics in driven excitable systems

Numerous studies have shown that strange nonchaotic attractors (SNAs) can be observed generally in quasiperiodically forced systems. These systems could be one- or high-dimensional maps, continuous-time systems, or experimental models. Recently introduced measures of complexity based on recurrence plots can detect the transitions from quasiperiodic to chaotic motion via SNAs in the previously cited systems. We study here the case of continuous-time systems and experimental models. In particular, we show the performance of the recurrence measures in detecting transitions to SNAs in quasiperiodically forced excitable systems and experimental time series.     

Deterministic and stochastic components of nonlinear Markov models with an application to decision making during the bailout votes 2008 (USA)

We apply a nonlinear Markov chain model to examine decision making in the US house of representatives during the period between the bailout votes of September 29 and October 3, 2008. We show how to determine deterministic and stochastic properties of the nonlinear model and, in doing so, estimate the strength of the attractors and the amplitudes of fluctuating forces that putatively influenced representatives’ decision making.     

Attractors of a randomly forced electronic oscillator

This paper examines an electronic oscillator forced by a pseudo-random noise signal. We give evidence of the existence of one or more random attractors for the system depending on noise amplitude and system parameters. These random attractors may appear to be random fixed points or random chaotic attractors. In the latter case, we observe a form of intermittent synchronization of the response of the system to the noise signal. We show how this can be understood as on–off intermittency in an extended system.     

Stochastic climate dynamics: Random attractors and time-dependent invariant measures

This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models’ global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sinaï-Ruelle-Bowen (SRB) measures.