, Volume 67, Issue 4, pp 2455-2465
Date: 11 Aug 2011

A novel bounded 4D chaotic system

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Abstract

This paper presents a novel bounded four-dimensional (4D) chaotic system which can display hyperchaos, chaos, quasiperiodic and periodic behaviors, and may have a unique equilibrium, three equilibria and five equilibria for the different system parameters. Numerical simulation shows that the chaotic attractors of the new system exhibit very strange shapes which are distinctly different from those of the existing chaotic attractors. In addition, we investigate the ultimate bound and positively invariant set for the new system based on the Lyapunov function method, and obtain a hyperelliptic estimate of it for the system with certain parameters.

Supported by the National Natural Science Foundation of China No. 61004015, the Research Fund for the Doctoral Program of Higher Education of China No. 20090032120034, and the Program for Changjiang Scholars and Innovative Research Team in University of China.