Dynamics of the polynomial differential systems with homogeneous nonlinearities and a star node

Ahmed Bendjeddou, Jaume Llibre, Tayeb Salhi

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)

Abstract

We consider the class of polynomial differential equations x=λx+Pn(x,y), y=λy+Qn(x,y), in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n>1 and λ≠0, i.e. the class of polynomial differential systems with homogeneous nonlinearities with a star node at the origin.We prove that these systems are Darboux integrable. Moreover, for these systems we study the existence and non-existence of limit cycles surrounding the equilibrium point located at the origin. © 2013 .
Original languageEnglish
Pages (from-to)3530-3537
JournalJournal of Differential Equations
Volume254
Issue number8
DOIs
Publication statusPublished - 15 Apr 2013

Keywords

  • Cubic system
  • Limit cycle
  • Star node

Fingerprint

Dive into the research topics of 'Dynamics of the polynomial differential systems with homogeneous nonlinearities and a star node'. Together they form a unique fingerprint.

Cite this