Journal of Guangxi Normal University(Natural Science Edition) ›› 2019, Vol. 37 ›› Issue (3): 96-105.doi: 10.16088/j.issn.1001-6600.2019.03.011

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Research on Complex Dynamics of a New 4D Hyperchaotic System

HONG Lingling, YANG Qigui*   

  1. School of Mathematics, South China University of Technology, Guangzhou Guangdong 510640, China
  • Online:2019-07-12 Published:2019-07-12

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Abstract: In this paper, based on the 3D Lorenz-like chaotic system, a linear feedback controller is designed and a new four-dimensional hyperchaos system with only two times nonlinear terms is proposed. This system has simple algebraic structure, but shows complex dynamic behavior, and it is proved theoretically that it is not equivalent to hyperchaotic Li system. In order to study the complex dynamics of the system, the stability of the system at the hyperbolic and non-hyperbolic equilibrium points is discussed in detail, and the Hopf bifurcation is strictly analyzed. The approximate expression and stability of the periodic orbit generated by the Hopf bifurcation are obtained. Furthermore, the Lyapunov exponent spectrum, Poincaré map and bifurcation diagram of the system are obtained by numerical simulation with the help of modern mathematical software, and the existence of the hyperchaotic attractor is verified.

Key words: hyperchaotic system, stability, Hopf bifurcation, complex dynamics, attractor

CLC Number: 

  • O415.5
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