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

Toshikazu Kuniya; Tarik Mohammed Touaoula; Toshikazu Kuniya; Tarik Mohammed Touaoula

doi:10.3934/mbe.2020375

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7332-7352. doi: 10.3934/mbe.2020375

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

Toshikazu Kuniya ^{1
,
,},
Tarik Mohammed Touaoula ²

1.
Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
2.
Départment de Mathématiques, Faculté des Sciences, Université de Tlemcen, Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, 13000, Tlemcen, Algérie

Received: 19 August 2020 Accepted: 19 October 2020 Published: 27 October 2020

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.
- distributed delay,
- bistable nonlinearity,
- global stability,
- Lyapunov functional,
- Allee effect
Citation: Toshikazu Kuniya, Tarik Mohammed Touaoula. Global stability for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7332-7352. doi: 10.3934/mbe.2020375

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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.

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