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On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations

Rezaiki Nabil, Boulfoul Amel

Journal of Applied Analysis

2024

Vol. 30, nr 1

35--50

In this paper,westudy the number of limit cycles bifurcated from the periodic orbits of a cubic uniform isochronous center with continuous and discontinuous quartic polynomial perturbations. Using the averaging theory of first order for continuous and discontinuous differential systems and comparing the obtained results, we show that the discontinuous systems have at least 6 more limit cycles than the continuous ones. This study needs some computations that have been verified using Maple.