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Estimating the bound for the generalized lorenz system

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Chinese Physics B 2010年第1期19卷 156-159页

作者：郑宇张晓丹 Department of Mathematics and Mechanics University of Science and Technology Beijing

A chaotic system is bounded, and its trajectory is confined to a certain region which is called the chaotic attractor. No matter how unstable the interior of the system is, the trajectory never exceeds the chaotic attractor. In the present paper, the sphere bound of the generalized lorenz system is given, based on the Lyapunov function and the Lagrange multiplier method. Furthermore, we show the actual parameters and perform numerical simulations.

关键词： chaos generalized lorenz system Lyapunov function Lagrange multiplier method

Estimating the ultimate bound and positively invariant set for a generalized lorenz system

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Journal of Chongqing University 2008年第2期7卷 151-154页

作者：舒永录张永浩 College of Mathematics and Physics Chongqing University

A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized lorenz *** derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized lorenz system,for all the positive values of system parameters a,b,and *** results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].

关键词： generalized lorenz system ultimate bound positively invariant set generalized Lyapunov function

BIDIRECTIONALLY COUPLED SYNCHRONIZATION OF THE generalized lorenz systemS

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Journal of systems Science & Complexity 2011年第3期24卷 433-448页

作者： Juan CHEN Jun-an LU Xiaoqun WU School of Mathematics and Statistics Wuhan University Wuhan 430072 China

Wu, Chen, and Cai （2007） investigated chaos synchronization of two identical generalized lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirec- tional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized lorenz systems. Some sufficient synchronization conditions for some special coupling matrices （diagonal ma- trices, so-called dislocated coupling matrices, and so on） are derived through rigorously mathematical theory. In particular, for the classical lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of lorenz system （Chaos, Solitons, and Fractals, 2005）. The criteria are then applied to four typical generalized lorenz systems in the numerical simulations for verification.

关键词： Bidirectionally-coupled chaos generalized lorenz system synchronization ultimate bound.

Chaos Synchronization of Master-slave Hyperbolic-type generalized lorenz systems via Linear State Error Feedback Control

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Chaos Synchronization of Master-slave Hyperbolic-type Genera...

A New lorenz-Like Chaotic Attractor and Its Synchronization

第二十七届中国控制会议

作者： Gui Zhifang 1,Wu Xiaofeng 1,2,3,Chen Yun 1 1.College of Electronic Engineering,Naval University of Engineering,Wuhan 430033,P.R.China 2.Guangzhou Navy Academy,Guangzhou 510430,P.R.China

This paper proposes the sufficient synchronization criteria for master and slave hyperbolic-type generalized lorenz systems via linear state error feedback *** algebraic synchronization criterion for the linear diagon... 详细信息

关键词： Chaos Synchronization generalized lorenz system Linear state error feedback

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A New Lorenz-Like Chaotic Attractor and Its Synchronization