Limit cycles of a class of generalized Liénard polynomial equations - Resultats de la cerca

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9 p, 763.1 KB

Limit cycles for a class of discontinuous generalized Liénard polynomial differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (UFSCar(Brazil). Department of Physics, Chemistry and Mathematics)
We divide R2 in l sectors S1, . . . , Sl, with l > 1 even. We define in R2 a discontinuous differential system such that in each sector Sk, for k = 1, . . . , l, is defined a smooth generalized Lienard polynomial differential equation ¨x + fi(x) ˙x + gi(x) = 0, i = 1, 2 alternatively, where fi and gi are polynomials of degree n−1 and m respectively. [...]
2013
Electronic journal of differential equations, Vol. 2013 Núm. 195 (2013) , p. 1-8

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6 p, 729.4 KB

Limit cycles of a class of generalized Liénard polynomial equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba (Algeria). Department of Mathematics)
We prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x.
2015 - DOI (Digital Object Identifier)

10.1007/s10883-014-9253-4
Journal of Dynamical and Control Systems, Vol. 21 (2015) , p. 189-192

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