单参数Chen系统的Hopf分岔及参数辨识  

Hopf Bifurcation and Parameter Identification of Chen System with a Single Parameter

作　　者：李德奎[1] 

机构地区：[1]定西师范高等专科学校数学系

出　　处：《辽宁大学学报（自然科学版）》2015年第1期15-23,共9页Journal of Liaoning University：Natural Sciences Edition

基　　金：国家自然科学基金项目(11161027);教育部科技研究重点项目(212180);定西师范高等专科学校青年人才资助项目

摘　　要：首先应用非线性动力学理论,分析单参数Chen系统平衡点的稳定性及Hopf分岔的存在性.并通过中心流形定理和范式理论,给出周期解稳定性和方向的表达式.其次,将系统的未知参数看成其状态变量,并根据状态观测器思想和微分方程稳定性理论,提出选择增益函数和构造辅助函数的方法,并设计系统线性组合部分未知参数的状态观测器.最后通过数值仿真验证理论分析的正确性.We analyze the stability of equilibria and the existence of Hopf bifurcation for Chen system with a single parameter, firstly, by using the theory of nonlinear dynamics. And through the center manifold theorem and the theory of paradigm, the stability of periodic solution and the expression of the direction are given. Secondly, we regard the unknown parameter of system as the state variable,propose a method of choosing gain function and structuring auxiliary function, and design the state observer for unknown parameter of system＇s linear combination, based on state observer thought and differential equation stability theory. Finally, the correctness of theoretical analysis is verified by some numerical simulations.

关 键 词：单参数Chen系统 HOPF分岔 状态观测器 

分 类 号：O415.5[理学—理论物理]