Global stability of a tridiagonal competition model with seasonal succession

Xizhuang Xie; Meixiang Chen; Xizhuang Xie; Meixiang Chen

doi:10.3934/mbe.2023262

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 6062-6083. doi: 10.3934/mbe.2023262

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Research article

Global stability of a tridiagonal competition model with seasonal succession

Xizhuang Xie ^,,
Meixiang Chen

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received: 03 December 2022 Revised: 05 January 2023 Accepted: 16 January 2023 Published: 18 January 2023

In this paper, we investigate a tridiagonal three-species competition model with seasonal succession. The Floquet multipliers of all nonnegative periodic solutions of such a time-periodic system are estimated via the stability analysis of equilibria. Together with the Brouwer degree theory, sufficient conditions for existence and uniqueness of the positive periodic solution are given. We further obtain the global dynamics of coexistence and extinction for three competing species in this periodically forced environment. Finally, some numerical examples are presented to illustrate the effectiveness of our theoretical results.
- tridiagonal competition model,
- seasonal succession,
- carrying simplex,
- Poincaré-map,
- global dynamics
Citation: Xizhuang Xie, Meixiang Chen. Global stability of a tridiagonal competition model with seasonal succession[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6062-6083. doi: 10.3934/mbe.2023262

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Abstract

In this paper, we investigate a tridiagonal three-species competition model with seasonal succession. The Floquet multipliers of all nonnegative periodic solutions of such a time-periodic system are estimated via the stability analysis of equilibria. Together with the Brouwer degree theory, sufficient conditions for existence and uniqueness of the positive periodic solution are given. We further obtain the global dynamics of coexistence and extinction for three competing species in this periodically forced environment. Finally, some numerical examples are presented to illustrate the effectiveness of our theoretical results.

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