非线性函数耦合的Chen吸引子网络的混沌同步

利用非对称非线性函数耦合混沌同步方法,讨论了Chen吸引子的混沌同步问题,数值模拟分析初始值和耦合强度因子的选择对于实现混沌同步的影响. 将非对称非线性函数耦合同步方法进一步推广发展到完全连接网络和由星形子网络构成的复杂大网络混沌同步的研究中. 提供了确定网络中神经元之间混沌同步状态稳定性的误差发展方程,并讨论各个耦合强度因子对网络同步稳定性过程的影响,给出了相应的稳定性范围. 通过数值模拟证明利用非线性函数作为耦合函数,实现完全连接网络、星形子网络构成大网络的混沌同步是有效的. 可以预测在网络的混沌同步 关键词： 非线性耦合函数 Chen吸引子 混沌同步 网络     

复系统Julia集的同步

非线性系统中的分形集——Julia集, 在工程技术中有着十分重要的应用,定义了不同系统间的Julia集同步的概念, 并引入一种非线性耦合的方法, 对同一系统不同参数的Julia集进行了有效的同步.并以多项式形式和三角函数形式的Julia集同步为例验证了该方法的有效性.     

Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added. Supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151) and the Innovative Team Program of Liaoning Educational Committee     

Synchronization of chaotic fractional-order systems via active sliding mode controller

In this paper, we propose a controller based on active sliding mode theory to synchronize chaotic fractional-order systems in master-slave structure. Master and slave systems may be identical or different. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Finally, three numerical simulations (synchronizing fractional-order Lü-Lü systems, synchronizing fractional order Chen-Chen systems and synchronizing fractional-order Lü-Chen systems) are presented to show the effectiveness of the proposed controller. The simulations are implemented using two different numerical methods to solve the fractional differential equations.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.     

一类不确定混沌系统的自适应同步

讨论了混沌系统的同步问题 .对一类不确定混沌系统 ,提出了一个新的自适应同步方法 ,可使响应系统在自适应控制器的控制下 ,实现与不确定混沌系统的同步 .最后给出了一个设计实例 .     

Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes

In this Letter, exponential synchronization of a complex network with nonidentical time-delayed dynamical nodes is considered. Two effective control schemes are proposed to drive the network to synchronize globally exponentially onto any smooth goal dynamics. By applying open-loop control to all nodes and adding some intermittent controllers to partial nodes, some simple criteria for exponential synchronization of such network are established. Meanwhile, a pinning scheme deciding which nodes need to be pinned and a simply approximate formula for estimating the least number of pinned nodes are also provided. By introducing impulsive effects to the open-loop controlled network, another synchronization scheme is developed for the network with nonidentical time-delayed dynamical nodes, and an estimate of the upper bound of impulsive intervals ensuring global exponential stability of the synchronization process is also given. Numerical simulations are presented finally to demonstrate the effectiveness of the theoretical results.     

Exact Boundary Synchronization by Groups for a Kind of System of Wave Equations Coupled with Velocities*

This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with velocities. These problems can not be solved directly by the usual HUM method for wave equations, however, by transforming the system into a first order hyperbolic system, the HUM method for 1-D first order hyperbolic systems, established by Li-Lu(2022) and Lu-Li(2022), can be applied to get the corresponding results.     

“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.