Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal

Minjuan Gao; Lijuan Chen; Fengde Chen; Minjuan Gao; Lijuan Chen; Fengde Chen

doi:10.3934/mbe.2024242

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 5499-5520. doi: 10.3934/mbe.2024242

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Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal

School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, Fujian, China

Academic Editor: Yang Kuang

Received: 21 December 2023 Revised: 03 February 2024 Accepted: 19 February 2024 Published: 19 March 2024

The dynamic behavior of a discrete-time two-patch model with the Allee effect and nonlinear dispersal is studied in this paper. The model consists of two patches connected by the dispersal of individuals. Each patch has its own carrying capacity and intraspecific competition, and the growth rate of one patch exhibits the Allee effect. The existence and stability of the fixed points for the model are explored. Then, utilizing the central manifold theorem and bifurcation theory, fold and flip bifurcations are investigated. Finally, numerical simulations are conducted to explore how the Allee effect and nonlinear dispersal affect the dynamics of the system.
- flip bifurcation,
- fold bifurcation,
- Allee effect,
- nonlinear dispersal
Citation: Minjuan Gao, Lijuan Chen, Fengde Chen. Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5499-5520. doi: 10.3934/mbe.2024242

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Abstract

The dynamic behavior of a discrete-time two-patch model with the Allee effect and nonlinear dispersal is studied in this paper. The model consists of two patches connected by the dispersal of individuals. Each patch has its own carrying capacity and intraspecific competition, and the growth rate of one patch exhibits the Allee effect. The existence and stability of the fixed points for the model are explored. Then, utilizing the central manifold theorem and bifurcation theory, fold and flip bifurcations are investigated. Finally, numerical simulations are conducted to explore how the Allee effect and nonlinear dispersal affect the dynamics of the system.

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