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BY 4.0 license Open Access Published by De Gruyter Open Access December 31, 2020

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

  • Manel Amdouni EMAIL logo and Farouk Chérif


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.


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Received: 2020-09-08
Accepted: 2020-12-18
Published Online: 2020-12-31

© 2020 Manel Amdouni et al., published by De Gruyter

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

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