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3 results on '"Salhi, Tayeb"'

1. On the Limit Cycles of the Piecewise Differential Systems Formed by a Linear Focus or Center and a Quadratic Weak Focus or Center

Author

Llibre, Jaume and Salhi, Tayeb

Subjects
Quadratic center, General Mathematics, Applied Mathematics, Linear focus, General Physics and Astronomy, Statistical and Nonlinear Physics, Linear center, Quadratic weak focus, Limit cycle, Discontinuous piecewise differential system
Abstract

While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the limit cycles of the discontinuous piecewise differential systems formed by one linear differential system and a quadratic polynomial differential system separated by one straight line. In this paper using the averaging theory up to seven order we prove that the discontinuous piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center separated by one straight line can have 8 limit cycles. More precisely, at every order of the averaging theory from order one to order seven we provide the maximum number of limit cycles that can be obtained using the averaging theory.

Published
2022

2. Limit Cycles of Piecewise-Continuous Differential Systems Formed by Linear and Quadratic Isochronous Centers II.

Author

Ghermoul, Bilal, Llibre, Jaume, and Salhi, Tayeb

Subjects
DIFFERENTIAL forms, LINEAR systems, LIMIT cycles, QUADRATIC forms, AFFINE transformations, ORBITS (Astronomy)
Abstract

We study the crossing periodic orbits and limit cycles of the planar piecewise-continuous differential systems separated by the straight-line x = 0 having in x > 0 the general quadratic isochronous center ẋ = − y + x 2 , ẏ = x (1 + y) after an affine transformation, and in x < 0 an arbitrary quadratic isochronous center except for the quadratic isochronous center ẋ = − y + x 2 − y 2 , ẏ = x (1 + 2 y) which has been studied in [Ghermoul et al., 2021]. For these piecewise-continuous differential systems the upper bound of crossing limit cycles is 2, and there are specific examples having one crossing limit cycle. [ABSTRACT FROM AUTHOR]

Published
2022
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3. Dynamics of the polynomial differential systems with homogeneous nonlinearities and a star node

Author

Bendjeddou, Ahmed, Llibre, Jaume, and Salhi, Tayeb

Subjects
*HOMOGENEOUS polynomials, *DIFFERENTIAL equations, *NONLINEAR theories, *DARBOUX transformations, *INTEGRABLE functions, *LIMIT cycles
Abstract

Abstract: We consider the class of polynomial differential equations , , in where and are homogeneous polynomials of degree and , i.e. the class of polynomial differential systems with homogeneous nonlinearities with a star node at the origin. We prove that these systems are Darboux integrable. Moreover, for these systems we study the existence and non-existence of limit cycles surrounding the equilibrium point located at the origin. [Copyright &y& Elsevier]

Published
2013
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