The bifurcation of limit cycles of two classes of cubic systems with homogeneous nonlinearities

Abstract

In this paper, we study the bifurcation of limit cycles of the periodic annulus of two classes of cubic isochronous systems. By using complete elliptic integrals of the first, second kinds and the Chebyshev criterion, we show that the upper bound for the number of limit cycles which appear from the periodic annuli of the two systems are at least three under cubic perturbations. Moreover, there exists a perturbation that give rise to exactly $i$ limit cycles bifurcating from the period annulus for each $i=0,1,2,3$.

Keywords

• limit cycle
• period annulus
• cubic perturbations