Aspects of bifurcation theory for piecewise-smooth, continuous systems

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Simpson, D. J. W.²  Meiss, J. D.¹ 

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

关键词: Bifurcation;    Border collision;    Discontinuous bifurcation;    Saddle-node;    Hopf;    Neimark-Sacker;   

DOI  :  10.1016/j.physd.2011.05.002

来源: Elsevier

【 摘 要 】

Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a surface on which the system is not smooth. Much of our understanding of these cases relies on a reduction to piecewise linearity near the border collision. We also review a number of codimension-two bifurcations in which nonlinearity is important. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free