一类具分布时滞和非单调双稳非线性的泛函微分方程的全局稳定性。

Global stability for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity.

机构信息

Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.

Départment de Mathématiques, Faculté des Sciences, Université de Tlemcen, Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, 13000, Tlemcen, Algérie.

出版信息

Math Biosci Eng. 2020 Oct 27;17(6):7332-7352. doi: 10.3934/mbe.2020375.

DOI:10.3934/mbe.2020375

PMID:33378899

Abstract

The present work is devoted to the global stability analysis for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity. First, we characterize some subsets of attraction basins of equilibria. Next, by Lyapunov functional and fluctuation method, we obtain a series of criteria for the global stability of equilibria. Finally, we illustrate our results by applying them to a problem with Allee effect.

摘要

本文致力于研究一类具有分布时滞和非单调双稳非线性的泛函微分方程的全局稳定性分析。首先，我们刻画了平衡点吸引域的一些子集。其次，通过李雅普诺夫泛函和涨落方法，我们得到了平衡点全局稳定性的一系列判据。最后，我们通过应用于具有阿利效应的问题来说明我们的结果。