Degenerate Hopf Bifurcations in Discontinuous Planar Systems

B. Coll, A. Gasull, R. Prohens

Research output: Contribution to journalArticleResearchpeer-review

108 Citations (Scopus)


We study the stability of a singular point for planar discontinuous differential equations with a line of discontinuities. This is done, for the most generic cases, by computing some kind of Lyapunov constants. Our computations are based on the so called (R,θ,p,q)-generalized polar coordinates, introduced by Lyapunov, and they are essentially different from the ones used in the smooth case. These Lyapunov constants are also used to generate limit cycles for some concrete examples. © 2001 Academic Press.
Original languageEnglish
Pages (from-to)671-690
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Jan 2001


Dive into the research topics of 'Degenerate Hopf Bifurcations in Discontinuous Planar Systems'. Together they form a unique fingerprint.

Cite this