Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed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.v2). 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.v2).

Abstract

Firstly, the author do dynamic analysis for reaction-diffusion Gilpin-Ayala competition model with Dirichlet boundary value, involved in harmful species. Existence of multiple stationary solutions is verified by way of Mountain Pass lemma, and the local stability result of the null solution is obtained by employing linear approximation principle. Secondly, the author utilize variational methods and LMI technique to deduce the LMI-based global exponential stability criterion on the null solution which becomes the unique stationary solution of the ecosystem with delayed feedback under a reasonable boundedness assumption on population densities. Particularly, LMI criterion is involved in free weight coefficient matrix, which reduces the conservatism of the algorithm. In addition, a new impulse control stabilization criterion is also derived. Finally, two numerical examples show the effectiveness of the proposed methods. It is worth mentioning that the obtained stability criteria of null solution presented some useful hints on how to eliminate pests and bacteria.

Subject Areas

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

Comments (1)

Comment 1
Received: 24 February 2021
Commenter: Ruofeng Rao
Commenter's Conflict of Interests: Author
Comment: Dear editor,
 This revision of my manuscript "Local and Global Stability Analysis for Gilpin-Ayala Competition Model Involved in Harmful Species Via LMI Approach and Variational Methods" (preprints202102.0050.v1) add a new theorem--Theorem 4.1, and English text is polished.
Best regards,
Ruofeng Rao, the author of Manuscript (preprints202102.0050)

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