Abstract
In this article, we study the limit cycles bifurcated from a Lienard system with a heteroclinic loop connecting two nilpotent saddles. We apply expansion theory of a first-order Melnikov function to investigate the number of limit cycles near the heteroclinic loop and the center, and by some perturbation theory we find 3 limit cycles with 7 different distributions. Last, the least upper bound of the number of limit cycles bifurcated from the annulus is given by an algebraic criterion developed in J. Differ. Equ. 251, 1656–1669 (2011).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.