新型混沌系统的Hopf分岔与复杂动力学分析  

Hopf Bifurcation and Complex Dynamics Analysis of a New Chaotic System

作　　者：刘宇 周艳[1,2] 郭碧垚 LIU Yu;ZHOU Yan;GUO Biyao(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Center for Applied Mathematical Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]内蒙古师范大学应用数学中心,呼和浩特010022

出　　处：《内蒙古农业大学学报（自然科学版）》2023年第2期89-94,共6页Journal of Inner Mongolia Agricultural University(Natural Science Edition)

基　　金：国家自然科学基金项目(11962025);内蒙古自治区联合基金项目(2019LH01002);内蒙古师范大学2022年度研究生科研创新基金项目(CXJJS22098);内蒙古师范大学基本科研业务费基金项目(2022JBXC013,2023JBBJ004)。

摘　　要：本文对一个新型类Lorenz系统的Hopf分岔进行研究。首先,基于类Lorenz系统的特征方程,并利用Routh-Hurwitz标准,分析了平衡态的局部稳定性,得到了系统的平衡点和Hopf分岔的存在条件,表明该系统中存在Hopf分岔。然后,利用Normal Form理论,计算得出了确定分岔周期解的稳定性和Hopf分岔方向的公式。最后,通过MATLAB进行数值模拟,得到系统时域波形图和相图,数值验证结果表明系统在参数变化下的稳定状态和不稳定状态,产生了混沌吸引子,与理论分析相印证,得到其有效性。The Hopf bifurcation of a new Lorenz-like system was studied in this paper.Based on the characteristic equation of Lorenz-like system,the local stability of equilibrium state was analyzed by using the Routh-Hurwitz criterion.The equilibrium point and the existence condition of the Hopf bifurcation were obtained.It showed that the Hopf bifurcation existed in the system.Then,by using the Normal Form theory,formulae for determining the stability of periodic bifurcation solutions and the Hopf bifurcation direction were obtained.Finally,numerical simulations were carried out by using the MATLAB software to obtain the time-domain waveform and phase diagram of the system.The numerical verification results showed that the system was in the stable and unstable state under the change of parameters,and the chaos attractor was generated,which was verified with theoretical analysis to obtain its effective-ness.

关 键 词：HOPF分岔 周期解 局部稳定性 类LORENZ系统 Normal Form理论 

分 类 号：O193[理学—数学]