Hyperchaotic attractors from a linearly controlled Lorenz system

被引：47
作者：
Yang, Qigui [1 ]
Zhang, Kangming [1 ]
Chen, Guanrong [2 ]
机构：
[1] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China
[2] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Hong Kong, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2009年 / 10卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Hyperchaos; Chaos; Lorenz system; Lyapunov exponent; Bifurcation; Period orbit; STATE-FEEDBACK CONTROL; EQUATION;
D O I：
10.1016/j.nonrwa.2008.02.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a four-dimensional (4D) continuous-time autonomous hyperchaotic system with only one equilibrium is introduced and analyzed. This hyperchaotic system is constructed by adding a linear controller to the second equation of the 3D Lorenz system. Some complex dynamical behaviors of the hyperchaotic system are investigated, revealing many interesting properties: (i) existence of periodic orbit with two zero Lyapunov exponents; (ii) existence of chaotic orbit with two zero Lyapunov exponents; (iii) chaos depending on initial value w(0); (iv) chaos with only one equilibrium; and (v) hyperchaos with only one equilibrium. Finally, two complete mathematical characterizations for 4D Hopf bifurcation are derived and studied. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1601 / 1617
页数：17
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