Piecewise linear differential systems with an algebraic line of separation

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We study the number of limit cycles of planar piecewise linear differential systems separated by a branch of an algebraic curve. We show that for each n (Formula presented) N there exist piecewise linear differential systems separated by an algebraic curve of degree n having [n/2] hyperbolic limit cycles. Moreover, when n = 2, 3, we study in more detail the problem, considering a perturbation of a center and constructing examples with 4 and 5 limit cycles, respectively. These results follow by proving that the set of functions generating the first order averaged function associated to the problem is an extended complete Chebyshev system in a suitable interval.

Original languageEnglish
Article number19
JournalElectronic Journal of Differential Equations
Volume2020
Publication statusPublished - 2020

Keywords

  • Algebraic separation
  • And phrases
  • ECT-system
  • Limit cycle
  • Piecewise linear differential system

Fingerprint

Dive into the research topics of 'Piecewise linear differential systems with an algebraic line of separation'. Together they form a unique fingerprint.

Cite this