一类Van Der Pol-Duffing模型的隐藏吸引子存在性问题  

Existence of Hidden Attractors for a Class of Van Der Pol Duffing Model

作　　者：聂家升 焦岑 吕小俊 Nie Jiasheng;Jiao Cen;Lv Xiaojun(Applied Technology College of Soochow University,Suzhou 215300,China)

机构地区：[1]苏州大学应用技术学院,江苏苏州215300

出　　处：《科学技术创新》2022年第10期37-40,共4页Scientific and Technological Innovation

基　　金：江苏省教育厅基金项目(21KJB110013);云南省教育厅科学研究基金(2020J0908)。

摘　　要：就目前的研究来说,隐藏吸引子是一个比较新颖的课题,而研究动力系统中隐藏吸引子的存在性问题是一项重要的研究课题。通过建立一个新颖的非线性Van Der Pol-Duffing振子模型,运用一项新的研究方法,即分析-数值方法,从而研究非线性动力系统中隐藏吸引子的存在性问题。基于经典的动力系统Hopf分支理论,根据Routh-Hurwitz判据讨论平衡点的稳定性,利用谐波线性化方法和分析-数值方法,分析并验证隐藏吸引子的存在性,最后通过数值模拟定位出隐藏吸引子。As far as the current research is concerned,the hidden attractor is a relatively new topic,and the study of the existence of hidden attractors in dynamical systems is an important research topic.By establishing a novel nonlinear van der Pol Duffing oscillator model and using a new research method,analytical numerical method,the existence of hidden attractors in nonlinear dynamic systems is studied.Based on the classical Hopf bifurcation theory of dynamical system,the stability of equilibrium point is discussed according to the Routh Hurwitz criterion.The existence of hidden attractor is analyzed and verified by harmonic linearization method and analysis numerical method.Finally,the hidden attractor is located by numerical simulation.

关 键 词：动力系统 隐藏吸引子 HOPF分支 谐波线性化 分析-数值方法 

分 类 号：O175.14[理学—数学]