Border collision bifurcations in 3D piecewise smooth chaotic circuit  

作　　者：Yinghui GAO Xiangying MENG Qishao LU 

机构地区：[1]School of Mathematics and System Sciences, LMIB of the Ministry of Education,Beihang University [2]Department of Biology, University of Maryland [3]School of Aeronautic Science and Engineering, Beihang University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第9期1239-1250,共12页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11272024,11371046,and 11372017);the Fundamental Research Funds for the Central Universities

摘　　要：A variety of border collision bifurcations in a three-dimensional （3D） piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.A variety of border collision bifurcations in a three-dimensional （3D） piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.

关 键 词：electrical circuit border collision bifurcation multiple crossing 

分 类 号：O19[理学—数学]