Diffusion-induced inhomogeneity in globally coupled oscillators: swing-by mechanism

It is shown that for random initial conditions, a large population of identical and sufficiently nonisochronous Stuart-Landau oscillators coupled globally and diffusively exhibits inhomogeneity in a resonant way as the diffusive coupling is intensified, where the diffusive coupling constant is real. A category of inhomogeneous (nonsynchronized) solutions is analytically shown to exist, which is either periodic or quasiperiodic.     

PERIODIC WINDOWS AND CHAOTIC TRANSIENT IN COUPLED MAP LATTICES

A class of special periodic windows in coupled Logistic lattice and its bifurcation behaviors versus the coupling strength are investigated, The system has long chaotic transient and the average transient length increases exponentially with respect to the system size.     

Transition between synchronization and chaos in doped GaAs/AlAs superlattices

The transition between chaotic and periodic regimes in spontaneous current oscillations of weakly coupled, doped GaAs/AlAs superlattices has been observed by varying the external d.c. bias. The chaotic current oscillations are observed for voltage ranges, which exhibit a large negative differential conductance in the time-averaged I–V characteristic. Since this system can be described by a spatially distributed, non-linear system with many degrees of freedom, the coupling between the degrees of freedom in the chaotic windows is repulsive, while in the periodic windows it is attractive.     

弱耦合映射系统在周期窗口内的行为

通过解析讨论及数值计算的验证,发现弱耦合映射系统的周期窗口只存在于耦合强度极小的范围内(对于3周期窗口大约为10^-3),这个范围可以定义为周期窗口的深度。在周期窗口内耦合映射的行为可以通过讨论少数几个模(相对简单的耦合三映射,实质是一维映射)而确定。耦合映射的第一Lyapunov指数随耦合强度增大的变化曲线呈锯齿形状。 关键词：     

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.     

Chaos out of internal noise in the collective dynamics of diffusively coupled cells

We study the transition from stochasticity to determinism in calcium oscillations via diffusive coupling of individual cells that are modeled by stochastic simulations of the governing reaction-diffusion equations. As expected, the stochastic solutions gradually converge to their deterministic limit as the number of coupled cells increases. Remarkably however, although the strict deterministic limit dictates a fully periodic behavior, the stochastic solution remains chaotic even for large numbers of coupled cells if the system is set close to an inherently chaotic regime. On the other hand, the lack of proximity to a chaotic regime leads to an expected convergence to the fully periodic behavior, thus suggesting that near-chaotic states are presently a crucial predisposition for the observation of noise-induced chaos. Our results suggest that chaos may exist in real biological systems due to intrinsic fluctuations and uncertainties characterizing their functioning on small scales.     

Coupling Effect of Ion Channel Clusters on Calcium Signalling

Based on a modified intracellular Ca^2＋ model involving diffusive coupling of two calcium ion channel dusters, the effects of coupling on calcium signalling are numerically investigated. The simulation results indicate that the diffusive coupling of dusters together with internal noise determine the calcium dynamics of single duster, and for either homogeneous or heterogeneous coupled dusters, the synchronization of dusters, which is important to calcium signalling, is enhanced by the coupling effect.     

Coupled trivial maps

The first nontrivial example of coupled map lattices that admits a rigorous analysis in the whole range of the strength of space interactions is considered. This class is generated by one-dimensional maps with a globally attracting superstable periodic trajectory that are coupled by a diffusive nearest-neighbor interaction.     

A self-organizing network in the weak-coupling limit

We prove the existence of spatially localized ground states of the diffusive Haken model. This model describes a self-organizing network whose elements are arranged on a d-dimensional lattice with short-range diffusive coupling. The network evolves according to a competitive gradient dynamics in which the effects of diffusion are counteracted by a localizing potential that incorporates an additional global coupling term. In the absence of diffusive coupling, the ground states of the system are strictly localized, i.e. only one lattice site is excited. For sufficiently small non-zero diffusive coupling , it is shown analytically that localized ground states persist in the network with the excitations exponentially decaying in space. Numerical results establish that localization occurs for arbitrary values of in one dimension but vanishes beyond a critical coupling _c(d), when d> 1. The one-dimensional localized states are interpreted in terms of instanton solutions of a continuum version of the model.     

Semi-passivity and synchronization of diffusively coupled neuronal oscillators

We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled Hindmarsh-Rose and Morris-Lecar oscillators. Finally we discuss possible “instabilities” in networks of oscillators induced by the diffusive coupling.     

Lattice limit cycle dynamics: Influence of long-distance reactive and diffusive mixing

The properties of global oscillations produced by coupled reactive stochastic discrete systems on a 2D lattice support are studied, taking into account the competitive influence of local and global mixing processes. Two types of global mixing are considered: reactive and diffusive. It is shown that in the case of diffusive mixing the increase in the diffusive coupling leads to a corresponding increase in the amplitude of the global oscillations. In the case of reactive mixing the competition of local-to-global effects leads to unexpected complex phenomena. Kinetic Monte Carlo simulations demonstrate that the amplitude of oscillations as a function of the mixing-reactive coupling presents an optimal value, which is attributed to the competitive effects between the local and global processes.     

Renormalization Group for Strongly Coupled Maps

Systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos. We show how the well-known renormalization group (RG) of unimodal maps can be extended to the coupled systems, and in particular to coupled map lattices (CMLs) with local diffusive coupling. The RG relation derived for CMLs is nonperturbative, i.e., not restricted to a particular class of configurations nor to some vanishingly small region of parameter space. After defining the strong-coupling limit in which the RG applies to almost all asymptotic solutions, we first present the simple case of coupled tent maps. We then turn to the general case of unimodal maps coupled by diffusive coupling operators satisfying basic properties, extending the formal approach developed by Collet and Eckmann for single maps. We finally discuss and illustrate the general consequences of the RG: CMLs are shown to share universal properties in the space-continuous limit which emerges naturally as the group is iterated. We prove that the scaling properly ties of the local map carry to the coupled systems, with an additional scaling factor of length scales implied by the synchronous updating of these dynamical systems. This explains various scaling laws and self-similar features previously observed numerically.     

Time-varying coupling-induced logical stochastic resonance in a periodically driven coupled bistable system

Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noise level. Here constant coupling is extended to time-varying coupling, and then we investigate the effect of time-varying coupling on LSR in a periodically driven coupled bistable system. When coupling intensity oscillates periodically with the same frequency with periodic force or relatively high frequency, the system successfully yields the desired logic output. When coupling intensity oscillates irregularly with phase disturbance, large phase disturbance reduces the area of optimal parameter region of coupling intensity and response speed of logic devices. Although the system behaves as a desired logic gate when the frequency of time-periodic coupling intensity is precisely equal to that of periodic force, the desired logic gate is not robust against tiny frequency difference and phase disturbance. Therefore, periodic coupling intensity with high frequency ratio is an optimal option to obtain a reliable and robust logic operation.     

Chaotic patterns in a coupled oscillator-excitator biochemical cell system

In this paper we examine dynamical modes resulting from diffusion-like interaction of two model biochemical cells. Kinetics in each of the cells is given by the ICC model of calcium ions in the cytosol. Constraints for one of the cells are set so that it is excitable. One of the constraints in the other cell - a fraction of activated cell surface receptors-is varied so that the dynamics in the cell is either excitable or oscillatory or a stable focus. The cells are interacting via mass transfer and dynamics of the coupled system are studied as two parameters are varied-the fraction of activated receptors and the coupling strength. We find that (i) the excitator-excitator interaction does not lead to oscillatory patterns, (ii) the oscillator-excitator interaction leads to alternating phase-locked periodic and quasiperiodic regimes, well known from oscillator-oscillator interactions; torus breaking bifurcation generates chaos when the coupling strength is in an intermediate range, (iii) the focus-excitator interaction generates compound oscillations arranged as period adding sequences alternating with chaotic windows; the transition to chaos is accompanied by period doublings and folding of branches of periodic orbits and is associated with a Shilnikov homoclinic orbit. The nature of spontaneous self-organized oscillations in the focus-excitator range is discussed. (c) 1999 American Institute of Physics.     

Dynamical behavior of the multiplicative diffusion coupled map lattices

We report a dynamical study of multiplicative diffusion coupled map lattices with the coupling between the elements only through the bifurcation parameter of the mapping function. We discuss the diffusive process of the lattice from an initially random distribution state to a homogeneous one as well as the stable range of the diffusive homogeneous attractor. For various coupling strengths we find that there are several types of spatiotemporal structures. In addition, the evolution of the lattice into chaos is studied. A largest Lyapunov exponent and a spatial correlation function have been used to characterize the dynamical behavior. (c) 1996 American Institute of Physics.     

A 795 nm gain coupled distributed feedback semiconductor laser based on tilted waveguides

The 795 nm distributed feedback lasers have great application in pumping the Rb D1 transition. In this paper, in order to realize specific 795 nm lasing, we designed tilted ridge distributed feedback lasers based on purely gain coupled effect induced by periodic current injection windows through changing the angle of the tilted ridge. The fabricated devices were cleaved into 2 mm-cavity-length, including 5 tilted angles. The peak output powers of all devices were above 30 m W.Single longitudinal mode lasing was realized in all tilted Fabry–Perot cavities using periodic current injection windows,with side mode suppression ratio over 30 d B. The total wavelength range covered 8.656 nm at 20℃. It was disclosed theoretically and experimentally that the output powers, threshold currents, and central wavelengths of the tilted ridge purely gain coupled DFB lasers were relevant to the tilted angles. The results will be instructive for future design of DFB laser arrays with different central wavelengths.     

Creation of spectral bands for a periodic domain with small windows

We consider a Schrödinger operator in a periodic system of strip-like domains coupled by small windows. As the windows close, the domain decouples into an infinite series of identical domains. The operator similar to the original one, and defined on one copy of these identical domains, has an essential spectrum. We show that once there is a virtual level at the threshold of this essential spectrum, the windows turn this virtual level into the spectral bands for the original operator. We study the structure and the asymptotic behavior of these bands.     

钾扩散耦合引起的心脏中螺旋波的变化

在某些情况下, 心肌细胞外的钾离子浓度是变化的, 钾离子的横向扩散会导致细胞外钾离子的聚集和产生钾扩散耦合, 用考虑钾扩散耦合的Luo-Rudy相I心脏模型研究了钾扩散耦合对螺旋波动力学的影响. 数值模拟结果表明: 当钾扩散耦合比较强时, 钾扩散耦合使细胞外钾离子浓度先升高, 然后做规则振荡, 导致螺旋波做无规则漫游; 观察到螺旋波的波臂宽度和频率随钾扩散耦合的强度增大而减小, 这样, 当钾扩散耦合足够强时, 钾扩散耦合可以消除螺旋波和时空混沌. 关键词： 钾扩散耦合 螺旋波 时空混沌     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.