Fifteen Limit Cycles Bifurcating from a Perturbed Cubic Center

Abstract

In this work, we study the bifurcation of limit cycles from the period annulus surrounding the origin of a class of cubic polynomial differential systems; when they are perturbed inside the class of all polynomial differential systems of degree six, we obtain at most fifteenth limit cycles by using the averaging theory of first order.

Modelling, Control Methods and Applications of Chaotic Oscillators

“…Menaceur et al [29] investigated the bifurcation of limit cycles from the period annulus surrounding the origin of a class of cubic polynomial diferential systems by using the averaging theory of frst order. In the literature of ordinary diferential equations, it is well-known that limit cycles can be yielded by perturbing a system which has a centre in a suitable manner so that limit cycles bifurcate in the perturbed system.…”