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Bifurcation analysis in a modified Leslie-Gower predator-prey model with fear effect and multiple delays
Shuo Yao1, Jingen Yang2, Sanling Yuan1
1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China.
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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