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Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 133--143 | DOI:10.5890/DNC.2025.03.008

Selma Ellaggoune$^1$, Khaireddine Fernane$^2$

$^{1}$ Department of Computer Sciences and Mathematics, Ecole Normale Superieure Assia Djebar, Constantine, Algeria

$^2$ University 8 Mai 1945, Guelma, Algeria

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Abstract

In this paper we estimate the maximum number of limit cycles that can bifurcate from an integrable non-linear quadratic ischronous center, when perturbed inside a class of Li\'{e}nard-like polynomial differential systems of arbitrary degree $n$. The main tool employed in this study is the averaging theory of first order.

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