Limit cycles of septic polynomial differential systems bifurcating from the periodic annulus of cubic center

Abstract

This paper focuses on investigating the maximum number of limit cycles bifurcating from the periodic orbits adapted to the cubic system given by ẋ=y−yx+a2,ẏ=−x+xx+a2,where a is a positive number with a≠1. The study specifically examines the perturbation of this system within the class of all septic polynomial differential systems. Our main result demonstrates that the first-order averaging theory associated with the perturbed system yields a maximum of twenty-two limit cycles.

Keywords

• Differential equations
• Mathematical operators
• Limit cycle
• Averaging method
• Periodic orbit
• Septic polynomial differential system