Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Existence and Local Stability of Stationary Solutions for Nonlinear Gilpin Ayala Competition Model with Dirichlet Boundary Value

Version 1 : Received: 18 September 2020 / Approved: 19 September 2020 / Online: 19 September 2020 (10:07:43 CEST)

How to cite: Rao, R. Existence and Local Stability of Stationary Solutions for Nonlinear Gilpin Ayala Competition Model with Dirichlet Boundary Value. Preprints 2020, 2020090456 (doi: 10.20944/preprints202009.0456.v1). Rao, R. Existence and Local Stability of Stationary Solutions for Nonlinear Gilpin Ayala Competition Model with Dirichlet Boundary Value. Preprints 2020, 2020090456 (doi: 10.20944/preprints202009.0456.v1).

Abstract

In this paper, the existence of two nontrivial stationary solutions for the nonlinear Gilpin Ayala two species competition model is given by using the mountain pass lemma, and the local stability criterion of the trivial solution is given by using Lyapunov function method. Based on the local stability criterion, we give some suggestions on how to avoid the population extinction. This is, when the population is on the verge of extinction, we should try our best to avoid the diffusion behavior and reduce the diffusion coefficient, otherwise the species are easy to go extinct. Numerical example shows the effectiveness of the proposed method.

Subject Areas

Gilpin Ayala competition model; Lyapunov function; Mountain Pass Lemma; Palais Smale condition; Dirichlet boundary value

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