(µ, η)-pseudo almost automorphic solutions of a new class of competitive Lotka-Volterra model with mixed delays

Nonautonomous Dynamical Systems

卷:7

Chérif Farouk¹  Amdouni Manel² 

[1] ISSATs and Laboratory of Mathematical Physic, Specials Functions and Applications, LR11ES35, Ecole Supérieure des Sciences et de Technologie de Hammam-Sousse, Université de Sousse, Sousse, Tunisia;

[2] MaPSFA, ISSAT, Université de Sousse, Sousse, Tunisia;

关键词: lotka-volterra;    (µ, η)-pseudo almost automorphic;    leray-schauder fixed point;    permanence;    stability;   

DOI  :  10.1515/msds-2020-0120

来源: DOAJ

【 摘 要 】

In the natural world, competition is an important phenomenon that can manifest in various generalized environments (economy, physics, ecology, biology,...). One of the famous models which is able to represent this concept is the Lotka-Volterra model. A new class of a competitive Lotka-Volterra model with mixed delays and oscillatory coefficients is investigated in this work. Thus, by using the (µ, η)-pseudo almost automorphic functions function class and the Leray-Schauder fixed-point theorem, it can be proven that solutions exist. In addition, in such situations, we have a number of species that coexist and all the rest will be extinct. Therefore, the study of permanence becomes unavoidable. Therefore, sufficient and new conditions are given in order to establish the permanence of species without using a comparison theorem. By the new Lyapunov function we prove the asymptotic stability for the considered model. Moreover, we investigate the globally exponential stability of the (µ, η)-pseudo almost automorphic solutions. In the end, an example is given to support theoretical result feasibility.

【 授权许可】

Unknown