Border collision bifurcations in two-dimensional piecewise smooth maps

被引:221
作者
Banerjee, S [1 ]
Grebogi, C
机构
[1] Indian Inst Technol, Dept Elect Engn, Kharagpur 721302, W Bengal, India
[2] Univ Maryland, Dept Math, Inst Plasma Res, College Pk, MD 20742 USA
[3] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA
关键词
D O I
10.1103/PhysRevE.59.4052
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps that cannot be classified among the generic cases like saddle-node, pitchfork, or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the need for the development of a theoretical framework and classification of the bifurcations resulting from border collision. We then present a systematic analysis of such bifurcations by deriving a normal form - the piecewise linear approximation in the neighborhood of the border. We show that there can be eleven qualitatively different types of border collision bifurcations depending on the parameters of the normal form, and these are classified under six cases. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. This theoretical framework will help in explaining bifurcations in all systems, which can be represented by two-dimensional piecewise smooth maps.
引用
收藏
页码:4052 / 4061
页数:10
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