GLOBALLY ATTRACTIVE AND POSITIVE INVARIANT SET OF THE LORENZ SYSTEM-Reference-Cited by-同舟云学术

GLOBALLY ATTRACTIVE AND POSITIVE INVARIANT SET OF THE LORENZ SYSTEM

Published:2006-03 Issue:03 Volume:16 Page:757-764
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

YU PEI¹,LIAO XIAOXIN²

Affiliation:

1. Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada

2. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China

Abstract

In this paper, based on a generalized Lyapunov function, a simple proof is given to improve the estimation of globally attractive and positive invariant set of the Lorenz system. In particular, a new estimation is derived for the variable x. On the globally attractive set, the Lorenz system satisfies Lipschitz condition, which is very useful in the study of chaos control and chaos synchronization. Applications are presented for globally, exponentially tracking periodic solutions, stabilizing equilibrium points and synchronizing two Lorenz systems.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127406015143

Reference12 articles.

1. A unifying definition of synchronization for dynamical systems

2. Attraktorlokalisierung des Lorenz-Systems

3. Attraktoreingrenzung für nichtlineare Systeme

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