Limit cycles for a class of polynomial differential systems

Jianyuan Qiao,Shuliang Shui

doi:10.14232/ejqtde.2016.1.9

Abstract

Limit cycles for a class of polynomial differential systems

Highlights

Introduction and main resultsOne of the main problems in the qualitative theory of real planar differential equations is to determinate the number of limit cycles for a given planar differential system
Regarding system (1.2) as a perturbation of a Hamiltonian system, the authors studied a class of Kukles systems having an invariant ellipse in the case of n ∈ {2k, 2k − 1} and obtained at most k − 2 limit cycles bifurcating from a unperturbed Hamiltonian center
In [18], using the averaging theory of first and second order, the authors studied the maximum number of limit cycles bifurcating from the periodic orbits of the linear center x = −y, y = x perturbed inside a class of generalized Kukles polynomial differential systems x = −y y

Summary

Introduction

Introduction and main resultsOne of the main problems in the qualitative theory of real planar differential equations is to determinate the number of limit cycles for a given planar differential system. The authors in [23] presented a class of quintic systems of the form (1.1) having an invariant ellipse with what small amplitude limit cycles bifurcating from the origin coexist.

Results

Conclusion