Journal of innovative applied mathematics and computational sciences
Volume 3, Numéro 1, Pages 49-65
2023-06-30
Periodic Solutions Of A Differential Perturbed System Via The Averaging Theory And The Melnikov Method
Authors : Karfes Sana . Hadidi Elbahi .
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 Melnikov method on the same system to see the 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
Differential system ; Periodic solution ; Averaging theory ; Melnikov's method
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