Jump to Content
Your Recent History
View Cart
Logged Out Log In
SIAM J. Appl. Dyn. Syst. 11, pp. 181-211 (31 pages)
Canonical Discontinuous Planar Piecewise Linear Systems
Alerts
Alert Me When Cited
Alert Me When Corrected
Tools
Download Citation
Add to MyScitation
Blog This Article
Print-Friendly
Research Toolkit
Share
Email Abstract
Connotea
CiteULike
del.icio.us
BibSonomy
Tweet this Article
Add to FacebookThe family of Filippov systems constituted by planar discontinuous piecewise linear systems with two half-plane linearity zones is considered. Under generic conditions that amount to the boundedness of the sliding set, some changes of variables and parameters are used to obtain a Liénard-like canonical form with seven parameters. This canonical form is topologically equivalent to the original system if one restricts one's attention to orbits with no points in the sliding set. Under the assumption of focus-focus dynamics, a reduced canonical form with only five parameters is obtained. For the case without equilibria in both open half-planes we describe the qualitatively different phase portraits that can occur in the parameter space and the bifurcations connecting them. In particular, we show the possible existence of two limit cycles surrounding the sliding set. Such limit cycles bifurcate at certain parameter curves, organized around different codimension-two Hopf bifurcation points. The proposed canonical form will be a useful tool in the systematic study of planar discontinuous piecewise linear systems, in which this paper is a first step.
© 2012 Society for Industrial and Applied Mathematics
RELATED DATABASES
To view database links for this article,
you need to log in.
KEYWORDS
ARTICLE DATA
History
Received July 01, 2011
Accepted November 15, 2011
Published online January 31, 2012
Accepted November 15, 2011
Published online January 31, 2012
Digital Object Identifier
For access to fully linked references, you need to log in.
ALL SIAM Content
Scitation
Google Scholar