时滞扰动类Lorenz系统的Hopf分岔  

Hopf bifurcation analysis of the disturbed Lorenz-like System with the delayed

作　　者：李文娟[1] 牛潇萌[1] 李旭超 俞元洪 Li Wenjuan;Niu Xiaomeng;Li Xvchao;Yu Yuanhong(School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China;Computer and Information Technology Institute, Chifeng University, Chifeng 024000, China)

机构地区：[1]赤峰学院数学与统计学院,内蒙古赤峰024000 [2]赤峰学院计算机与信息工程学院,内蒙古赤峰024000

出　　处：《纯粹数学与应用数学》2017年第5期475-485,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11561001);内蒙古自然科学基金(2014MS0101);内蒙古高等学校科研基金(NJZY17301)

摘　　要：通过非线性动力学理论,对时滞类Lorenz系统在平衡点的稳定性问题和发生Hopf分岔的条件进行了研究.首先计算得到系统的平衡点,然后通过分析系统在平衡点处的相应特征方程根的分布,得到系统在平衡点局部渐近稳定和产生Hopf分岔的时滞临界点.以时滞为分叉参数,研究了时滞系统存在Hopf分岔的条件.最后,利用Matlab程序进行仿真验证所得结论与理论分析一致.本文的结论是对一些已有文献研究成果的推广.In this paper,we analyze the stability and Hopf bifurcation condition of the system at its balance by using the nonlinear dynamics theory.The equilibrium point is obtained and then critical point of the delay for local stability of the equilibrium and existence of local Hopf bifurcation is also obtained by analyzing distribution of roots of the corresponding characteristic equation.the condition for the existence of Hopf bifurcation of this delay system is studied by taking delay as bifurcation parameter.Furthermore,by Matlab program some numerical simulations were given to show the correctness of the obtained conclusion.This paper extends the research achievements in the cited literature.

关 键 词：时滞 类LORENZ系统 稳定性 HOPF分岔 

分 类 号：O175[理学—数学]