Delayed feedback control and bifurcation analysis of Rossler chaotic system

被引:40
作者
Ding, Yuting [1 ]
Jiang, Weihua [1 ]
Wang, Hongbin [1 ]
机构
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
基金
中国国家自然科学基金;
关键词
Delayed feedback control; Hopf bifurcation; Chaos; Rossler system; DIFFERENTIAL EQUATIONS; TIME; SYNCHRONIZATION; MODEL;
D O I
10.1007/s11071-010-9681-y
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
In this paper, from the view of stability and chaos control, we investigate the Rossler chaotic system with delayed feedback. At first, we consider the stability of one of the fixed points, verifying that Hopf bifurcation occurs as delay crosses some critical values. Then, for determining the stability and direction of Hopf bifurcation we derive explicit formulae by using the normal-form theory and center manifold theorem. By designing appropriate feedback strength and delay, one of the unstable equilibria of the Rossler chaotic system can be controlled to be stable, or stable bifurcating periodic solutions occur at the neighborhood of the equilibrium. Finally, some numerical simulations are carried out to support the analytic results.
引用
收藏
页码:707 / 715
页数:9
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