一类三阶混沌系统的分支分析与混沌控制

Chaotic Control and Bifurcation Analysis of A Three Order Chaotic System

从稳定性与混沌控制的角度,研究了时滞对具反馈控制的三阶混沌系统动力学性质的影响.首先,研究时滞对系统平衡点稳定性的影响以及Hopf分支的存在性.其次,应用中心流形理论和规范型方法,得到了决定分支周期解的稳定性和方向的详细计算公式.通过设计合适的反馈增益和时滞,混沌振荡转变为稳定的不动点或稳定的周期轨.最后,用数值模拟验证了理论结果的有效性.

From the view of stability and chaos control,the effect of delay on the dynamics of a three order chaotic system with delayed feedback is investigated.Firstly,the effect of delay on the equilibrium points and the existence of local Hopf bifurcation is considered.Secondly,by using the center manifold theory and normal form method,the explicit formulas determining the stability,direction of bifurcating periodic solutions are derived.By designing appropriate feedback strength and delay,chaotic oscillation is converted into a stable equilibrium or a stable periodic orbit.Finally,some numerical simulations are carried out to support the analytic results.