Browsing by Author "Bendjeddou, Ahmed"

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    Coexistence of three limit cycles for a septic polynomial differential systems
    (Inderscience Publishers, 2020) Grazem, Mohamed; Bendjeddou, Ahmed; Cheurfa, Rachid
    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. © 2020 Inderscience Enterprises Ltd.. All rights reserved
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    Systems having liouvillian first integrals and Non-Algebraic limit cycles
    (Tsing Hua University, 2021) Grazem, Mohamed; Bendjeddou, Ahmed; Cheurfa, Rachid
    We consider the class of polynomial differential equations ẋ = Pm (x, y)+Pm+n (x, y), ẏ = Qm (x, y)+ Qm+n (x, y) for m, n ≥ 1 and where Pi and Qi are homogeneous polynomials of degree i. Inside this class, we identify a new subclass of Liouvillian integrable systems, under suitable conditions such Liouvillian integrable systems can have at most one limit cycle, and when it exists, is non-algebraic and hyperbolic. Then we study the general systems of the systems studied in [9], which allow us to find the necessary and suffi cient conditions for the existence and non-existence of limit cycles