<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The main goal of this paper is to provide the maximum number of crossing limit cycles of two different families of discontinuous piecewise linear differential systems. More precisely we prove that the systems formed by two regions, where, in one region we define a linear center and in the second region we define a Hamiltonian system without equilibria can exhibit three crossing limit cycles having two or four intersection points with the cubic of separation. After we prove that the systems formed by three regions, where, in two noadjacent regions we define a Hamiltonian system without equilibria, and in the third region we define a center, can exhibit six crossing limit cycles having four and two simultaneously intersection points with the cubic of separation.</p>
</abstract>

The main goal of this paper is to provide the maximum number of crossing limit cycles of two different families of discontinuous piecewise linear differential systems. More precisely we prove that the systems formed by two regions, where, in one region we define a linear center and in the second region we define a Hamiltonian system without equilibria can exhibit three crossing limit cycles having two or four intersection points with the cubic of separation. After we prove that the systems formed by three regions, where, in two noadjacent regions we define a Hamiltonian system without equilibria, and in the third region we define a center, can exhibit six crossing limit cycles having four and two simultaneously intersection points with the cubic of separation.

Limit cycles of discontinuous piecewise linear differential systems formed by centers or Hamiltonian without equilibria separated by irreducible cubics

Université Mohamed El Bachir El Ibrahimi

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The main goal of this paper is to provide the maximum number of crossing limit cycles of two different families of discontinuous piecewise linear differential...

Limit cycles of discontinuous piecewise linear differential systems formed by centers or Hamiltonian without equilibria separated by irreducible cubics

Published Online: Jan 29, 2021

Page range: 248 - 276

Received: May 07, 2020

Accepted: Dec 23, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0017

Keywords
Limit cycles, Discontinuous piecewise linear differential systems, Linear centers, Linear Hamiltonian systems, Irreducible cubic curves

© 2021 Loubna Damene et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Limit cycles of discontinuous piecewise linear differential systems formed by centers or Hamiltonian without equilibria separated by irreducible cubics

Published Online: Jan 29, 2021

Page range: 248 - 276

Received: May 07, 2020

Accepted: Dec 23, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0017

KeywordsLimit cycles, Discontinuous piecewise linear differential systems, Linear centers, Linear Hamiltonian systems, Irreducible cubic curves

© 2021 Loubna Damene et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Limit cycles, Discontinuous piecewise linear differential systems, Linear centers, Linear Hamiltonian systems, Irreducible cubic curves