Stability Study of a Holling-II Type Model and Leslie-Gower Modified with Diffusion and Time Delays in Dimension 3
Tia Kessé Thiban,
Nindjin Aka Fulgence,
Okou Hypolithe,
N’Guessan Tetchi Albin
Issue:
Volume 6, Issue 6, December 2018
Pages:
167-185
Received:
4 December 2018
Accepted:
10 January 2019
Published:
14 February 2019
DOI:
10.11648/j.ajam.20180606.11
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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.
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. U...
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