一个新三维类洛伦兹系统的最终有界集和正向不变集及其在同步中的应用

J4 ›› 2010, Vol. 45 ›› Issue (9): 83-89.

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The ultimate bound and positively invariant set of a new Lorenz-like chaotic system and its application in chaos synchronization

YANG Hong-liang1, ZHANG Fu-chen2*, SHU Yong-lu2, LI Yun-chao3

1. College of Information Science, Linyi Normal University, Linyi 276005, Shandong, China;
2. College of Mathematics and Physics, Chongqing University, Chongqing 400044, China;
3. Department of Mathematics, Northwest University, Xi’an 710127, Shaanxi,China

Received:2009-11-03 Online:2010-09-16 Published:2010-10-12

Abstract

Abstract:

The ultimate bound and positively invariant set of a new Lorenz-like system was investigated by constructing a positively definite and radically unbounded Lyapunov function and optimation theory. For this system, the three-dimensional ellipsoidal estimation and two-dimensional estimation about x-z were obtained. Then the upper bound about x,y,z was applied to the chaos synchronization to design a simple linear controller,and its complete synchronization was studied. Numerical simulations were presented to show the effectiveness of the proposed scheme.

Key words: ultimate bound; positively invariant set; chaotic synchronization; numerical simulations

YANG Hong-liang1, ZHANG Fu-chen2*, SHU Yong-lu2, LI Yun-chao3. The ultimate bound and positively invariant set of a new Lorenz-like chaotic system and its application in chaos synchronization[J].J4, 2010, 45(9): 83-89.