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基于脉冲控制下的复杂时滞动力网络的鲁棒同步

ISSN号：0254-0053
期刊名称：力学季刊
时间：0
页码：28-32
语言：中文
分类：O317[理学—一般力学与力学基础;理学—力学] O231[理学—运筹学与控制论;理学—数学]
作者机构：[1]上海大学上海市应用数学和力学研究所,上海200072
相关基金：国家自然科学基金项目（60474071,10672094和10832006）,教育部高等学校博士点专项科研基金（200802800015）,上海市教委科技发展基金（06AZ101）,上海市重点学科建设工程（Y0103）和上海大学系统生物基金
相关项目：具有脉冲效应耦合时滞系统动力学及其在神经动力学中的应用

关键词：鲁棒脉冲同步, 复杂时滞动力网络, 混沌FHN神经元振子, robust synchronization, complex delayed dynamical networks, chaotic FHN neuron oscillators

中文摘要：

近年来复杂网络已经引起了科学和工程技术等各个领域的广泛关注，尤其是复杂网络中的非线性动力学行为，以及网络的拓扑结构如何影响它的动力学行为的研究，已成为当前一项极其重要的战略课题。本文主要讨论基于脉冲控制下复杂时滞动力网络的同步动力学，应用时滞动力系统的脉冲控制理论，给出了复杂时滞动力网络的一些简单而又一般的鲁棒同步化准则，这些准则能够提供一个新的和有效的控制方法来同步一个任意给定的时滞动力网络到一个期望的同步态，进一步地将所获得的结果应用到由混沌FHN神经元振子为动力节点所构成的一个具有近邻耦合结构的复杂动力网络，数值模拟表明了所获理论结果的正确性和控制方法的有效性。

英文摘要：

Complex networks have recently attracted increasing attention from various fields of science and engineering. Especially, the study of nonlinear dynamical behaviors in complex dynamical networks, as well as how network topological structure influences its dynamical behaviors, has currently become a strategic topic of great significant. The present paper is mainly concerned with the synchronization dynamics of complex delayed dynamical networks via impulsive control. Based on the impulsive control theory on delayed dynamical systems, some simple yet generic criteria were derived for robust synchronization of complex delayed dynamical networks. It shows that these criteria can provide a novel and effective control approach to synchronize an arbitrary given delayed dynamical network to a desired synchronization state. Furthermore, the theoretical results were applied to a typical nearest neighbor coupled network composed of chaotic FHN neuron oscillators. Finally, the numerical simulations were carried out to verify the theoretical results, and also demonstrate the effectiveness of the proposed control techniques.

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