Local Bifurcation Analysis and Global Dynamics Estimation of a Novel 4-Dimensional Hyperchaotic System

Author:

Zhou Leilei12,Chen Zengqiang123,Wang Jiezhi3,Zhang Qing3

Affiliation:

1. College of Computer and Control Engineering, Nankai University, Tianjin 300353, P. R. China

2. Key Lab. of Intelligent Robots of Tianjin, Tianjin 300353, P. R. China

3. College of Science, Civil Aviation University of China, Tianjin 300300, P. R. China

Abstract

In this paper, we present a novel 4-dimensional (4D) smooth quadratic autonomous hyperchaotic system with complex dynamics. In order to investigate the dynamics evolution of the system, the Lyapunov exponent spectrum, bifurcation diagram and various phase portraits are provided. The local dynamics of this hyperchaotic system, such as the stability, pitchfork bifurcation, and Hopf bifurcation of equilibrium point, are analyzed by using the center manifold theorem and bifurcation theory. About the global dynamics, the ultimate bound sets of the system are found by combining the Lyapunov function method and appropriate optimization method. Numerical simulations are given to demonstrate the emergence of the two bifurcations and show the ultimate boundary regions.

Funder

Natural Science Foundation of China

Tianjin Nature Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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