On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities

Jaume Llibre, Jiang Yu, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

We consider the class of polynomial differential equations x = λx + P n (x, y), y = μy + Q n (x, y) in R 2 where P n (x, y) and Q n (x, y) are homogeneous polynomials of degree n > 1 and λ ≠ μ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations, we study the existence and nonexistence of limit cycles surrounding the node localized at the origin of coordinates. © 2014 World Scientific Publishing Company.
Original languageEnglish
Article number1450065
JournalInternational Journal of Bifurcation and Chaos
Volume24
Issue number5
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Homogeneous nonlinearities
  • Limit cycle
  • Node
  • Polynomial differential equations

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