Border collision bifurcations in 3D piecewise smooth chaotic circuit

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• 作者：Yinghui Gao ; Xiangying Meng ; Qishao Lu
• 关键词：Key wordselectrical circuit ; border collision bifurcation ; multiple crossing
• 刊名：Applied Mathematics and Mechanics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：37
• 期：9
• 页码：1239-1250
• 全文大小：404 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mechanics
  Mathematical Modeling and IndustrialMathematics
  Chinese Library of Science
  
• 出版者：Shanghai University, in co-publication with Springer
• ISSN：1573-2754
• 卷排序：37

文摘

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.