Invariant manifolds for nonsmooth systems

被引:29
作者
Weiss, D. [2 ]
Kuepper, T. [1 ]
Hosham, H. A. [1 ]
机构
[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany
[2] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany
关键词
Invariant manifold; Nonlinear piecewise dynamical systems; Invariant cones; Periodic orbits; Generalized Hopf bifurcation; GENERALIZED HOPF-BIFURCATION; PIECEWISE-LINEAR SYSTEMS; LIMIT-CYCLE BIFURCATION; CONES;
D O I
10.1016/j.physd.2011.07.012
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
For piecewise smooth systems we describe mechanisms to obtain a similar reduction to a lower dimensional system as has been achieved for smooth systems via the center manifold approach. It turns out that for nonsmooth systems there are invariant quantities as well which can be used for a bifurcation analysis but the form of the quantities is more complicated. The approximation by piecewise linear systems (PWLS) provides a useful concept. In the case of PWLS, the invariant sets are given as invariant cones. For nonlinear perturbations of PWLS the invariant sets are deformations of those cones. The generation of invariant manifolds and a bifurcation analysis establishing periodic orbits are demonstrated; also an example for which multiple cones exist is provided. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:1895 / 1902
页数:8
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