Abstract
In this paper, the problem of limit cycle bifurcation is investigated by perturbing a class of integrable systems with a homoclinic loop. Under the assumption that the homoclinic loop passes through a degenerate singular point at the origin, the asymptotic expansion of the Melnikov function along the level curves of the first integral inside the homoclinic loop is studied near the loop. Meanwhile, the formulas for the first coefficients in the expansion are given, which can be used to study the number of limit cycles near the homoclinic loop. Finally, an example is provided to demonstrate the obtained results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
