Limit Cycles of the Generalized Polynomial Liénard Differential Systems

Limit Cycles of the Generalized Polynomial Liénard Differential Systems

Year:    2016

Author:    Amel Boulfoul, Amar Makhlouf

Annals of Applied Mathematics, Vol. 32 (2016), Iss. 3 : pp. 221–233

Abstract

Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Liénard differential systems $$\begin{cases} \dot{x}= y + ϵh^1_l (x) + ϵ^2h^2_l (x),  \\ \dot{y}= −x − ϵ(f^1_n (x)y^{2p+1}+ g^1_m(x)) + ϵ^2 (f^2_n(x)y^{2p+1}+ g^2_m(x)), \end{cases}$$ which bifurcate from the periodic orbits of the linear center $\dot{x} = y,$ $\dot{y}= −x,$ where $ϵ$ is a small parameter. The polynomials $h^1_l$ and $h^2_l$ have degree $l;$ $f^1_n$ and $f^2_n$ have degree $n;$ and $g^1_m,$ $g^2_m$ have degree $m.$ $p ∈ \mathbb{N}$ and [·] denotes the integer part function.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2016-AAM-20639

Annals of Applied Mathematics, Vol. 32 (2016), Iss. 3 : pp. 221–233

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    limit cycle periodic orbit Liénard differential system averaging theory.

Author Details

Amel Boulfoul

Amar Makhlouf