Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Local and Global Stability Analysis for Gilpin-Ayala Competition Model Involved in Harmful Species Via LMI Approach and Variational Methods

Version 1 : Received: 31 January 2021 / Approved: 1 February 2021 / Online: 1 February 2021 (14:55:25 CET)
Version 2 : Received: 24 February 2021 / Approved: 24 February 2021 / Online: 24 February 2021 (11:05:19 CET)

How to cite: Rao, R. Local and Global Stability Analysis for Gilpin-Ayala Competition Model Involved in Harmful Species Via LMI Approach and Variational Methods. Preprints 2021, 2021020050 (doi: 10.20944/preprints202102.0050.v1). Rao, R. Local and Global Stability Analysis for Gilpin-Ayala Competition Model Involved in Harmful Species Via LMI Approach and Variational Methods. Preprints 2021, 2021020050 (doi: 10.20944/preprints202102.0050.v1).

Abstract

In this paper, stability of reaction-diffusion Gilpin-Ayala competition model with Dirichlet boundary value, involved in harmful species, was investigated. Employing Mountain Pass Lemma and linear approximation principle results in the local stability criterion of the null solution of the ecosystem which owns at least three stationary solutions. On the other hand, globally asymptotical stability criterion for the null solution of the ecosystem was derived by variational methods and LMI approach. It is worth mentioning that the stability criteria of null solution presented some useful hints on how to eliminate pests and bacteria. Finally, two numerical examples show the effectiveness of the proposed methods.

Keywords

Gilpin-Ayala competition model; LMI approach; Mountain Pass lemma; variational methods; Markovian jumping

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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