A new 5D hyperchaotic system based on modified generalized Lorenz system

被引：60

作者：

Yang, Qigui ^{[1
]}

Bai, Meili ^{[1
]}

机构：

[1] South China Univ Technol, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China

来源：

NONLINEAR DYNAMICS | 2017年 / 88卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Hyperchaos; Chaos; Coexisting attractor; Lyapunov exponents; Bifurcation; Stability; POSITIVE LYAPUNOV EXPONENTS; CHAOTIC SYSTEM; ATTRACTORS;

D O I：

10.1007/s11071-016-3238-7

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

This paper reports a new five-dimensional (5D) hyperchaotic system with three positive Lyapunov exponents, which is generated by adding a linear controller to the second equation of a 4D system that is obtained by coupling of a 1D linear system and a 3D modified generalized Lorenz system. This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest are the observations that the hyperchaotic system has a hyperchaotic attractor with three positive Lyapunov exponents under a unique equilibrium, three or infinite equilibria, and there are three types of coexisting attractors of this new 5D hyperchaotic system. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, Poincar, projections and power spectrum verifies the existence of the hyperchaotic and chaotic attractors. Moreover, stability of hyperbolic or non-hyperbolic equilibria and two complete mathematical characterization for 5D Hopf bifurcation are rigorously studied. Finally, some electronic circuits are designed to implement the 5D hyperchaotic system.

引用

页码：189 / 221

页数：33

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