Abstract

We consider an integrable non-Hamiltonian system, which belongs to the quadratic Kukles differential systems. It has a center surrounded by a bounded period annulus. We study polynomial perturbations of such a Kukles system inside the Kukles family. We apply averaging theory to study the limit cycles that bifurcate from the period annulus and from the center of the unperturbed system. First, we show that the periodic orbits of the period annulus can be parametrized explicitly through the Lambert function. Later, we prove that at most one limit cycle bifurcates from the period annulus, under quadratic perturbations. Moreover, we give conditions for the non-existence, existence, and stability of the bifurcated limit cycles. Finally, by using averaging theory of seventh order, we prove that there are cubic systems, close to the unperturbed system, with 1 and 2 small limit cycles.

Full Text
Paper version not known

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 call

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.