Isochronicity of bi-centers for symmetric quartic differential systems

Abstract

<p style='text-indent:20px;'>In this paper we investigate the simultaneous existence of isochronous centers for a family of quartic polynomial differential systems under four different types of symmetry. Firstly, we find the normal forms for the system under each type of symmetry. Next, the conditions for the existence of isochronous bi-centers are presented. Finally, we study the global phase portraits of the systems possessing isochronous bi-centers. The study shows the existence of seven non topological equivalent global phase portraits, where three of them are exclusive for quartic systems under such conditions.</p>