Bifurcation analysis in a modified Leslie-Gower predator-prey model with fear effect and multiple delays

Shuo Yao; Jingen Yang; Sanling Yuan; Shuo Yao; Jingen Yang; Sanling Yuan

doi:10.3934/mbe.2024249

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 5658-5685. doi: 10.3934/mbe.2024249

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Bifurcation analysis in a modified Leslie-Gower predator-prey model with fear effect and multiple delays

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
College of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China

Received: 21 January 2024 Revised: 03 March 2024 Accepted: 22 March 2024 Published: 19 April 2024

In this paper, we explored a modified Leslie-Gower predator-prey model incorporating a fear effect and multiple delays. We analyzed the existence and local stability of each potential equilibrium. Furthermore, we investigated the presence of periodic solutions via Hopf bifurcation bifurcated from the positive equilibrium with respect to both delays. By utilizing the normal form theory and the center manifold theorem, we investigated the direction and stability of these periodic solutions. Our theoretical findings were validated through numerical simulations, which demonstrated that the fear delay could trigger a stability shift at the positive equilibrium. Additionally, we observed that an increase in fear intensity or the presence of substitute prey reinforces the stability of the positive equilibrium.
- Leslie-Gower predator-prey model,
- fear effect,
- multiple delays,
- Hopf bifurcation,
- stability analysis
Citation: Shuo Yao, Jingen Yang, Sanling Yuan. Bifurcation analysis in a modified Leslie-Gower predator-prey model with fear effect and multiple delays[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5658-5685. doi: 10.3934/mbe.2024249

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Abstract

In this paper, we explored a modified Leslie-Gower predator-prey model incorporating a fear effect and multiple delays. We analyzed the existence and local stability of each potential equilibrium. Furthermore, we investigated the presence of periodic solutions via Hopf bifurcation bifurcated from the positive equilibrium with respect to both delays. By utilizing the normal form theory and the center manifold theorem, we investigated the direction and stability of these periodic solutions. Our theoretical findings were validated through numerical simulations, which demonstrated that the fear delay could trigger a stability shift at the positive equilibrium. Additionally, we observed that an increase in fear intensity or the presence of substitute prey reinforces the stability of the positive equilibrium.

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