On the limit cycles of polynomial vector field

J. Llibre, G. Świrszcz

Research output: Contribution to journalArticleResearchpeer-review

27 Citations (Scopus)

Abstract

In this paper we study the limit cycles which can bifurcate from the periodic orbits of the center located at the origin of the quadratic polynomial di®erential system x = -y(1+x), y= x(1+x), and of the cubic polynomial di®erential system x = -y(1-x2-y2), y= x(1-x 2-y2), when we perturb them in the class of all polynomial vector fields with quadratic and cubic homogenous nonlinearities, respectively. For doing this study we use the averaging theory. Copyright © 2011 Watam Press.
Original languageEnglish
Pages (from-to)203-214
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume18
Issue number2
Publication statusPublished - 8 Feb 2011

Keywords

  • Averaging method
  • Center
  • Limit cycle
  • Periodic orbit
  • Reversible center

Fingerprint Dive into the research topics of 'On the limit cycles of polynomial vector field'. Together they form a unique fingerprint.

Cite this