Article ID Journal Published Year Pages File Type
1703294 Applied Mathematical Modelling 2015 16 Pages PDF
Abstract

In this study, we consider the center problem and the bifurcation of limit cycles for a cubic system that lies in a symmetrical vector field about the origin. By analyzing and calculating the focal values (or the Lyapunov constant), we obtain the conditions where two equilibrium points, (1, 1) and (−1, −1), become a pair of simultaneous centers. Moreover, six limit cycles, including three stable limit cycles, can bifurcate from (1, 1) under a specific condition. From the symmetric quality, (−1, −1) can also bifurcate into six limit cycles by simultaneous Hopf bifurcation, which is an interesting result.

Related Topics
Physical Sciences and Engineering Engineering Computational Mechanics
Authors
, , ,