Periodic solutions of a differential perturbed system via the averaging theory and the Melnikov method

Abstract

In this paper, we will study the maximum number of limit cycles of a perturbed differential system with respect to its parameters which appear in the system specially on the degree of the polynomials. For this we will use two methods namely the averaging theory of first order and the method of Melnikov on the same system to provide an upper bound for the number of periodic solutions which can bifurcate from the center with ε = 0. In the end, we will present some numerical examples in order to illustrate the theoretical results given by the averaging theory and Melnikov one.

Keywords

• Periodic solution
• Differential system
• Averaging theory
• Melnikov’s method