Rssler原型4系统的Hopf分岔及幅值控制  

Hopf Bifurcation and Amplitude Control of an Rssler Prototype-4 System

作　　者：张中华[1] 付景超[1] 

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《数学的实践与认识》2016年第23期225-234,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11201057);吉林省科技发展计划项目(20130101065JC);博士科研启动基金项目(BSJXM-201427)

摘　　要：主要研究了一类Rssler原型4系统的Hopf分岔行为及极限环幅值控制问题.首先,利用Hopf分岔理论讨论系统发生Hopf分岔的条件,利用规范形理论判定系统的Hopf分岔类型,并给出极限环幅值算式;然后,对系统施加非线性反馈控制器,判定受控系统的Hopf分岔类型,并给出极限环幅值算式,讨论控制参数对极限环幅值的影响.最后,对讨论结果进行数值仿真,通过理论与仿真结果得出结论:非线性控制器可以改变极限环幅值大小,但不能改变Hopf分岔位置.This paper is concerned with Hopf bifurcation analysis and amplitude control of the Roessler prototype-4 system. Firstly, the condition of Hopf bifurcation is dicussed based on Hopf bifurcation theory, and the type of Hopf bifurcation is studied based on normal form, thus the amplitude of limit cycle is obtained by calculation. Then a nonlinear feedback controller is applied to the original system, the type of Hopf bifurcation and the amplitude of limit cycle of controlled system are investigated, and the effect of control parameter on the amplitude of limit cycle is discussed. Finally, numerical simulation results supporting the theoretical analysis are given, the theoretical results and the simulations show that the amplitude of limit cycle of the nonlinear controller can be changed, but the point of Hopf bifurcation can＇t be changed.

关 键 词：Roessler原型4系统 HOPF分岔 规范型 极限环 幅值控制 

分 类 号：O19[理学—数学]