Stability and Hopf bifurcation of a Lorenz-like system

被引：8
|
作者：
Wu, Ranchao [1 ]
Fang, Tianbao [1 ]
机构：
[1] Anhui Univ, Sch Math, Hefei 230601, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 262卷
基金：
高等学校博士学科点专项科研基金;
关键词：
Lyapunov exponent; Chaotic attractor; Hopf bifurcation; Normal form theory; CHAOTIC SYSTEM; ATTRACTOR; EQUATION;
D O I：
10.1016/j.amc.2015.04.072
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Hopf bifurcation is one of the important dynamical behaviors. It could often cause some phenomena, such as quasiperiodicity and intermittency. Consequently, chaos will happen due to such dynamical behaviors. Since chaos appears in the Lorenz-like system, to understand the dynamics of such system, Hopf bifurcation will be explored in this paper. First, the stability of equilibrium points is presented. Then Hopf bifurcation of the Lorenz-like system is investigated. By applying the normal form theory, the conditions guaranteeing the Hopf bifurcation are derived. Further, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also presented. Finally, numerical simulations are given to verify the theoretical analysis. It is found that Hopf bifurcation could happen when conditions are satisfied. The stable bifurcating periodic orbit is displayed. Chaos will also happen when parameter further increases. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：335 / 343
页数：9
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