Title: Coexistence of three limit cycles for a septic polynomial differential systems

Authors: Mohamed Grazem; Ahmed Bendjeddou; Rachid Cheurfa

Addresses: Department of Mathematics, University of Setif, 19000 Setif, Algeria; Department of Mathematics, University of Boumerdes, 35000 Boumerdes, Algeria ' Department of Mathematics, University of Setif, 19000 Setif, Algeria ' Department of Mathematics, University of Setif, 19000 Setif, Algeria

Abstract: The existence of limit cycles is interesting and very important in applications. It is a key to understand the dynamic of polynomial differential systems. The aim of this paper is to investigate a class of planar differential systems of degree seven. Under some suitable conditions, the existence of three limit cycles two of them are non-algebraic while the third is algebraic is proved. Furthermore, these limit cycles are explicitly given in polar coordinates. Some examples are presented in order to illustrate the applicability of our results.

Keywords: planar polynomial differential system; first integral; periodic orbits; algebraic and non-algebraic limit cycle.

DOI: 10.1504/IJDSDE.2020.107809

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.3, pp.249 - 267

Received: 16 Mar 2018
Accepted: 23 Oct 2018
Published online: 22 Jun 2020 *

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