“Hopf/homoclinic”簇放电和“SubHopf/homoclinic"簇放电之间的同步

以修正过的Morris-Lecar神经元模型为例,讨论了“Hopf/homoclinic”簇放电和“SubHopf/homoclinic"簇放电之间的同步行为.首先,分别考察了同一拓扑类型的两个耦合簇放电神经元的同步行为,发现“Hopf/homoclinic”簇放电比“SubHopf/homoclinic”簇放电达到膜电位完全同步所需要的耦合强度小,即前者比后者更容易达到膜电位完全同步.其次,对这两个不同拓扑类型的簇放电神经元的耦合同步行为进行了讨论.通过数值分析发现随着耦合强度的增加,两种不同类型的簇放电首先达到簇放电同步,然后当耦合强度足够大时甚至可以达到膜电位完全同步,并且同步后的放电类型更接近容易同步的簇放电类型,即“Hopf/homoclinic”簇放电.然而令人奇怪的是此时慢变量并没有达到完全同步,而是相位同步;慢变量之间呈现为一种线性关系.这一点和现有文献的结果截然不同.     

H∞ stochastic synchronization for master–slave semi‐Markovian switching system via sliding mode control

In this article, synchronization problem of master–slave system with phase‐type semi‐Markovian switching is investigated via sliding mode control scheme. By utilizing a supplementary variable technique and a plant transformation, the master–slave semi‐Markovian switching system can be equivalently expressed as its associated Markovian switching system. Then an integral sliding surface is constructed to guarantee stochastic synchronization of master–slave semi‐Markovian switching system, and the suitable controller is synthesized to ensure that the trajectory of the closed‐loop error system can be driven onto the prescribed sliding mode surface. Finally, numerical simulations are presented to show the effectiveness of the proposed sliding‐mode design scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 430–441, 2016     

Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization (FPS) in drive-response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.     

The dynamics of a symmetric coupling of three modified quadratic maps

We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-l, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.     

一类具有Markov性质的混沌系统的构造

本文构造了一类具有Markov性质的分段扩张线性映射, 计算表明其具有正的李雅普诺夫指数. 通过理论分析, 证明了其极限分布是均匀分布, 并给出了其最小周期的计算公式. 通过分析符号熵测度应用于此系统时的具体涵义, 指出该系统的复杂度与系统的最小周期之间存在着矛盾关系, 说明了此系统具有可控的复杂度并给出了其复杂度随系统参数变化时的理论极限公式. 通过统计测试和复杂度测试表明, 此系统产生的混沌序列服从均匀分布, 而通过参数的调整该系统的符号熵可以接近其理论极限, 而与Logistic映射和斜帐篷映射的基于近似熵和符号熵的对比实验可知, 本文所提系统具有更高的复杂度, 并有更长的最小周期. 这表明此系统比较适合用于构造保密通信系统. 关键词： 混沌 Markov性质 复杂度 均匀分布     

Interference of Quantum Chaotic Systems in Phase Space

We investigate the interference of a kicked harmonic oscillator in phase space.With the measure of interference defined in Lee and Jeong[Phys.Rev.Lett.106(2011)220401],we show that interference increases more rapidly in the chaotic regime than in the regular regime,and that the sub-Planck structure is of importance for the decoherence time in the chaotic regime.We also find that interference plays an important role in energy transport between the kicking fields and the kicked harmonic oscillator.     

Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.     

一类扩张了的软弹簧型Duffing方程的紊动性态

本文用Melnikov函数方法讨论了一类扩张了的软弹簧型Duffing方程(k=1,2,3,…)在周期激励下的紊动现象.给出了出现二阶同宿切的条件.文中所采用的方法对于不能给出并宿轨道的显式的系统的研究是非常有用的.     

Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay

This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay. The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated. Meanwhile, based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems, a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks. Finally, the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.     

Dynamical analysis,circuit realization,and application in pseudorandom number generators of a fractional-order laser chaotic system

A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.