Periodic orbits and bifurcations in discontinuous systems with a hyperbolic boundary

被引：3

作者：

Li L. ^{[1
]}

Luo A.C.J. ^{[2
]}

机构：

[1] Department of Mathematics, Huzhou University, Huzhou, 313000, Zhejiang

[2] Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, 62026-1805, IL

来源：

International Journal of Dynamics and Control | 2017年 / 5卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Bifurcation; Discontinuous system; G-function; Hyperbolic boundary; Periodic orbit;

D O I：

10.1007/s40435-016-0246-x

中图分类号：

学科分类号：

摘要：

The periodic orbits and bifurcations in a class of second-order discontinuous systems with a hyperbolic boundary are studied in this paper. Specifically, a periodically forced discontinuous system described by three different linear subsystems is considered mainly to demonstrate the methodology. Analytical conditions for the reachability of local flows in each sub-domain and the passability of flows on the hyperbolic boundary are developed first. Then, through the return mapping structure of motions, the periodic orbits with or without sliding motions are analytically predicted, and the corresponding bifurcation analyses are carried out. Finally, numerical illustrations of periodic orbits are presented and the G-function is proposed to show the analytical criteria. The results obtained in this paper can be applied to the sliding mode control in discontinuous dynamical systems. © 2016, Springer-Verlag Berlin Heidelberg.

引用

页码：513 / 529

页数：16

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