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Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle
Version 1
: Received: 11 July 2021 / Approved: 12 July 2021 / Online: 12 July 2021 (12:05:12 CEST)
Version 2 : Received: 5 August 2021 / Approved: 5 August 2021 / Online: 5 August 2021 (11:33:07 CEST)
Version 2 : Received: 5 August 2021 / Approved: 5 August 2021 / Online: 5 August 2021 (11:33:07 CEST)
A peer-reviewed article of this Preprint also exists.
Rao, R. Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle. Mathematics 2021, 9, 1943. Rao, R. Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle. Mathematics 2021, 9, 1943.
Abstract
This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.
Keywords
Minimax principle; linear approximation theory; ecosystem; steady state solution
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Ruofeng Rao
Commenter's Conflict of Interests: Author
This is my newly-modified version for my original manuscript "Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle" ( doi: 10.20944/preprints202107.0253.v1 ). Here, I only introduce three main changes :
1. In the proof of Theorem 3.1, some details are added ;
2. The condition (A1) is relaxed to allow a larger range of parameter values ;
3. In the final section, some further considerations are presented.
Best regards,
Ruofeng Rao, the author,
E-mail: ruofengrao@163.com; ruofengrao@cdnu.edu.cn
August 5, 2021, in China