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

<p>The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit cycles for a family of polynomial differential systems of degree 6<italic>k</italic> + 1, <italic>k</italic> ∈ ℕ*, with the non-elementary singular point. Under some suitable conditions, we show our system exhibiting two non algebraic or two algebraic limit cycles explicitly given. To illustrate our results we present some examples.</p>
</abstract>

The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit cycles for a family of polynomial differential systems of degree 6k + 1, k ∈ ℕ*, with the non-elementary singular point. Under some suitable conditions, we show our system exhibiting two non algebraic or two algebraic limit cycles explicitly given. To illustrate our results we present some examples.

Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Department of Mathematics, University Ferhat Abbas Sétif 1

Tatra Mountains Mathematical Publications

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

The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit...

Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Published Online: Jan 01, 2022

Page range: 33 - 46

Received: Nov 13, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0018

Keywords
Algebraic and non–algebraic limit cycle, planar polynomial differential system, first integral

© 2021 Mathematical Institute, Slovak Academy of Sciences

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

Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Published Online: Jan 01, 2022

Page range: 33 - 46

Received: Nov 13, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0018

KeywordsAlgebraic and non–algebraic limit cycle, planar polynomial differential system, first integral

© 2021 Mathematical Institute, Slovak Academy of Sciences

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

Keywords
Algebraic and non–algebraic limit cycle, planar polynomial differential system, first integral