Cyclicity of (1,3)-switching FF type equilibria

Xingwu Chen, Jaume Llibre, Weinian Zhang

Research output: Contribution to journalArticleResearch

Abstract

© 2019 American Institute of Mathematical Sciences. All rights reserved. Hilbert’s 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). Correspondingly, the same question for polynomial discontinuous differential systems is also interesting. Recently, it was proved that the cyclicity of (1, 2)-switching FF type equilibria is at least 5. In this paper we prove that the cyclicity of (1, 3)-switching FF type equilibria with homogeneous cubic nonlinearities is at least 3.
Original languageEnglish
Pages (from-to)6541-6552
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume24
DOIs
Publication statusPublished - 1 Dec 2019

Keywords

  • Cyclicity
  • Discontinuous differential system
  • Hopf bifurcation
  • Limit cycle

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