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border collision bifurcations in 3D piecewise smooth chaotic circuit

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Applied Mathematics and Mechanics(English Edition) 2016年第9期37卷 1239-1250页

作者： Yinghui GAO Xiangying MENG Qishao LU School of Mathematics and System Sciences LMIB of the Ministry of EducationBeihang University Department of Biology University of Maryland School of Aeronautic Science and Engineering Beihang University

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

A NEW SIMPLE 2-D PIECEWISE LINEAR MAP

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Journal of Systems Science & Complexity 2010年第2期23卷 379-389页

作者： Zeraoulia ELHADJ Julien Clinton SPROTT Department of Mathematics University of Tébessa Department of Physics University of Wisconsin

A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their stability, observation of a new chaotic attractors obtained via border collision bifurcation. An important resuk about coexisting chaotic attractors is also numerically studied and discussed.

关键词： border collision bifurcation new chaotic attractor piecewise linear map.

Dynamical Analysis of Nonlinear bifurcation in Current-Controlled Boost Converter

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Journal of Electronic Science and Technology of China 2007年第4期5卷 352-357页

作者： Quan-Min Niu Bo Zhang Yan-Ling Li Radar Academy Air Force Wuban 410019 China University of Electronic Science and Technology of China Chengdu 610054 China National University of Singapore

Based on the bifurcation theory in nonlinear dynamics, this paper analyzes quantitatively period solution dynamic characteristic. In particular, the ones of period-1 and period-2 solutions are deeply studied. From locus of Jacobian matrix eigenvalue, we conclude that the bifurcations between period-1 and period-2 solutions are pitchfork bifurcations while the bifurcations between period-2 and period-3 solutions are border collision bifurcations. The double period bifurcation condition is verified from complex plane locus of eigenvalues, furthermore, the necessary condition occurred pitchfork bifurcation is obtained from the cause of border collision bifurcation.

关键词： Boost converter border collision bifurcation eigenvalue Jacobian matrix period-doubling bifurcation.