On the Limit Cycles of a Class of Generalized Kukles Polynomial Differential Systems via Averaging Theory

Abstract

We apply the averaging theory of first and second order to a class of generalized Kukles polynomial differential systems to study the maximum number of limit cycles of these systems.

On Behavior of the Periodic Orbits of a Hamiltonian System of Bifurcation of Limit Cycles

“…Also, Makhlouf and Menaceur [7] studied the maximum number for the more generalized polynomial Kukles differential systems in the form…”

Limit Cycles of a Class of Polynomial Differential Systems Bifurcating from the Periodic Orbits of a Linear Center

“…In [6], Chavarriga et al studied the maximum number of small amplitude limit cycles for Kukles systems which can coexist with some invariant algebraic curves. By averaging theory, bifurcation of limit cycles for a family of perturbed Kukles differential systems was studied in [7][8][9][10][11]. In [8], Llibre and Mereu studied the maximum number of limit cycles of the Kukles polynomial differential systems…”