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Impact of fear-induced group defense in a Monod–Haldane type prey–predator model

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Abstract

In this paper, a predator–prey model with fear-induced group defense and Monod–Haldane functional response is considered. We establish a connection between fear effect and group defense by incorporating anti-predator sensitivity and emphasizing their impact on the dynamics of the model. Our analysis shows that increasing anti-predator sensitivity lowers the threshold for initiating group defense, leading to faster adoption of prey defense strategies. The preliminary results include positivity, boundedness, and persistence. We find that under certain thresholds, anti-predator sensitivity can sustain species persistence; otherwise, predators may face extinction. Changes in anti-predator sensitivity significantly influence system dynamics, notably affecting the quantity and stability of equilibrium points. We provide a comprehensive analysis of the global properties of both boundary and interior equilibrium points. Additionally, the system undergoes Transcritical, Saddle-node and Hopf bifurcation by considering the anti-predator sensitivity as a bifurcation parameter and Bogdanov–Takens bifurcation with respect to the prey birth rate and the anti-predator sensitivity. Numerical simulations support our theoretical findings. Our study highlights the complex interplay of fear effect, group defense, and anti-predator sensitivity in predator–prey dynamics. These results may provide valuable biological insights into predator–prey interactions.

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Acknowledgements

This work is supported by the Natural Science Foundation of China (11672074), the Natural Science Foundation of Fujian Province (2022J01192)and the Young Lecturer Education Research Project of Fujian Province (JAT220043).

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  1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, Fujian, People’s Republic of China

    Xiaohui Chen & Wensheng Yang

  2. FJKLMAA and Center for Applied Mathematics of Fujian Province (FJNU), Fuzhou, 350117, Fujian, People’s Republic of China

    Wensheng Yang

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Chen, X., Yang, W. Impact of fear-induced group defense in a Monod–Haldane type prey–predator model. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02101-8

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