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Limit cycles of Liénard polynomial systems type by averaging method

Moroccan Journal of Pure and Applied Analysis

Volume 6 (2020): Issue 1 (June 2020)

By: Amel Boulfoul and Nawal Mellahi

Open Access

|May 2020

Abstract

We apply the averaging theory of first and second order for studying the limit cycles of generalized polynomial Linard systems of the form

$\dot{x} = y - 1 (x) y, \dot{y} = - x - f (x) - g (x) y - h (x) y^{2},$ \dot x = y - 1\left( x \right)y,\,\,\dot y = - x - f\left( x \right) - g\left( x \right)y - h\left( x \right){y^2},

where l(x) = ∊l₁(x) + ∊²l₂(x), f (x) = ∊ f₁(x) + ∊²f₂(x), g(x) = ∊g₁(x) + ∊²g₂(x) and h(x) = ∊h₁(x) + ∊²h₂(x) where l_k(x) has degree m and f_k(x), g_k(x) and h_k(x) have degree n for each k = 1, 2, and ∊ is a small parameter.

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Articles in this issue

DOI: https://doi.org/10.2478/mjpaa-2020-0001 | Journal eISSN: 2351-8227

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Language: English

Page range: 1 - 15

Submitted on: Nov 27, 2019

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Accepted on: Feb 25, 2020

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Published on: May 29, 2020

Published by: Sciendo

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Linard differential system,

Periodic orbit,

Averaging theory

Related subjects:

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics

© 2020 Amel Boulfoul, Nawal Mellahi, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 6 (2020): Issue 1 (June 2020)