Browsing by Author "Mellahi , Nawal"

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    On The Maximum Number Of Limit Cycles Of Generalized Polynomial Liénard Differential Systems Via Averaging Theory*
    (Applied Mathematics E-Notes, 20(2020), 167-187, 2020) Boulfoul , Amel; Mellahi , Nawal
    In this paper, we apply the averaging theory of rst and second order for studying the limit cycles of generalized polynomial Liénard systems of the form x = y - l(x)y, y = -x - f(x) - g(x)y - h(x)y2 - p(x)y3 , where l(x) = ϵl1(x) + ϵ2l2(x) , f(x) = f1(x) + ϵ2f2(x) , g(x) = ϵg1(x) + ϵ2g2(x) ,h(x) = ϵh1(x) + 2h2(x) and p(x) = ϵp1(x) + ϵ2p2(x)where lᴷ(x) has degree m , fᴷ(x) , gᴷ(x),hᴷ(x) and pᴷ(x) have degree n for each k = 1, 2, and ϵ is a small parameter.