Volume 6, Issue 6, December 2018, Page: 167-185
Stability Study of a Holling-II Type Model and Leslie-Gower Modified with Diffusion and Time Delays in Dimension 3
Tia Kessé Thiban, Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët Boigny University of Abidjan Cocody, Abidjan, Ivory Coast
Nindjin Aka Fulgence, Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët Boigny University of Abidjan Cocody, Abidjan, Ivory Coast
Okou Hypolithe, Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët Boigny University of Abidjan Cocody, Abidjan, Ivory Coast
N’Guessan Tetchi Albin, Research and Formation Unit of Mathematics and Computer Science, Félix Houphouët Boigny University of Abidjan Cocody, Abidjan, Ivory Coast
Received: Dec. 4, 2018;       Accepted: Jan. 10, 2019;       Published: Feb. 14, 2019
DOI: 10.11648/j.ajam.20180606.11      View  105      Downloads  71
Abstract
This current paper investigates a predator-prey model from Holling-II type and Leslie Gower modified with diffusion and two time delays in dimension three. Firstly, we demonstrate that its solutions are positive and globally bounded. Secondly, we study the local stability of six equilibria points of from one is located within the relevant domain. Under certain conditions, it reveals that among the equilibria points, some are locally stable. Finally, we focus on the global stability of the positive interior equilibrium point. We show that the global stability set out due to the lack of time delays is kept until a certain threshold value of time delays above which a change in the stability is observed. Thus, the global convergence analysis towards the positive interior equilibrium point demonstrate the importance and impacts of the time delay in the stability of our model.
Keywords
Holling-2, Leslie-Gower, Boundedness, Lyapunov’s Functional, Equilibrium Point, Local Stability, Global Stability, Time Delay
To cite this article
Tia Kessé Thiban, Nindjin Aka Fulgence, Okou Hypolithe, N’Guessan Tetchi Albin, Stability Study of a Holling-II Type Model and Leslie-Gower Modified with Diffusion and Time Delays in Dimension 3, American Journal of Applied Mathematics. Vol. 6, No. 6, 2018, pp. 167-185. doi: 10.11648/j.ajam.20180606.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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