Dynamical analysis of a predator-prey system with fear-induced dispersal between patches

Jin Zhong; Yue Xia; Lijuan Chen; Fengde Chen; Jin Zhong; Yue Xia; Lijuan Chen; Fengde Chen

doi:10.3934/mbe.2025042

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 5: 1159-1184. doi: 10.3934/mbe.2025042

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Dynamical analysis of a predator-prey system with fear-induced dispersal between patches

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

Received: 26 February 2025 Revised: 18 March 2025 Accepted: 03 April 2025 Published: 09 April 2025

In this paper, a patchy model in which the migration is induced by the fear effect on the predator was investigated. By applying dynamical theory, the complete study on persistence of the system and the local/global stability of equilibria were discussed. Choosing the diffusion coefficient $ D_1 $ as the bifurcation parameter, transcritical bifurcation occurring near the trivial equilibrium was demonstrated. We concluded that low dispersal is favorable for the coexistence of both species, but large dispersal leads to the extinction of species. There is an optimal diffusion coefficient to make the density of the prey population reach its maximum. In addition, the level of fear effect $ k $ and the maximum fear cost $ \eta $ are beneficial to the total population density of prey.
- fear effect,
- dispersal,
- predator-prey,
- global stability,
- bifurcation
Citation: Jin Zhong, Yue Xia, Lijuan Chen, Fengde Chen. Dynamical analysis of a predator-prey system with fear-induced dispersal between patches[J]. Mathematical Biosciences and Engineering, 2025, 22(5): 1159-1184. doi: 10.3934/mbe.2025042

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Abstract

In this paper, a patchy model in which the migration is induced by the fear effect on the predator was investigated. By applying dynamical theory, the complete study on persistence of the system and the local/global stability of equilibria were discussed. Choosing the diffusion coefficient $ D_1 $ as the bifurcation parameter, transcritical bifurcation occurring near the trivial equilibrium was demonstrated. We concluded that low dispersal is favorable for the coexistence of both species, but large dispersal leads to the extinction of species. There is an optimal diffusion coefficient to make the density of the prey population reach its maximum. In addition, the level of fear effect $ k $ and the maximum fear cost $ \eta $ are beneficial to the total population density of prey.

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