New Estimations of Bounds for the Chu Chaotic System

Article Preview

Abstract:

This paper is concerned with positive invariant set for the Chu chaotic system using a technique combing the generalized Lyapunov function theory and maximum principle. For this chaotic system, some new ellipsoid estimations and a cylindrical domain estimation of the globally exponentially attractive set for all the positive parameters values of the system are derived without existence assumptions via employing inequality techniques and the continuous extension principle.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

196-199

Citation:

Online since:

October 2011

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] Leonov G., Bunin A. and Koksch N., in: Attract or localization of the Lorenz system[J]. ZAMM 1987, 67 (2): 649-656.

Google Scholar

[2] Liao X.X., Luo H.G., Fu Y.L., etc, in: Positive Invariant Set and the Globally Exponentially Attractive Set of Lorenz System Group[J]. Science in China–E 2007, 37(6): 757-769.

Google Scholar

[3] Qin W.X. and Chen G.R., in: On the Boundedness of Solutions of the Chen System[J]. Journal of Mathematical Analysis and Application, 2007, 329(1): 445-451.

Google Scholar

[4] Li D. M., Wu X.Q. and Lu J. A., in: Estimating the Ultimate Bound and Positively Invariant Set for the Hyperchaotic Lorenz-Haken System[J]. Chaos, Solitons and Fractals, 2009, 39: 1290-1296.

DOI: 10.1016/j.chaos.2007.06.038

Google Scholar

[5] Chu Y.D., Li X.F. and Zhang J.G., etc, in: Computer Simulation and Circuit Implementation for a New Autonomous Chaotic System[J]. Journal of Sichuan University, 2007, 44 (3): 596-602.

Google Scholar

[6] Shu Y.L., Xu H.X. and Zhao Y.H., in: Estimating the Ultimate Bound and Positively Invariant Set for a New Chaotic System and Its Application in Chaos Synchronization[J]. Chaos, Solitons and Fractals, 2009, 42: 2852-2857.

DOI: 10.1016/j.chaos.2009.04.003

Google Scholar

[7] Wang G.H. and Jian J.G., in: Globally Exponentially Attractive Set and Controlling of a New Chaotic System. Int. Conf. Machine Learning and Cybernetics, 2010, 2: 916-921.

DOI: 10.1109/icmlc.2010.5580602

Google Scholar

[8] S. Lefchetz: Differential Equations: Geometric Theory[M]. New York: Inter-science Publishers (1963).

Google Scholar