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Spatiotemporal dynamics of a delayed diffusive ratio-dependent predator–prey model with fear effect

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Abstract

By considering that there is a delay on the impact of fear to the growth rate of prey, we consider a delayed diffusive predator–prey model with fear effect. First, we give some conditions of the existence of the equilibria. Then, sufficient conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are also obtained. Furthermore, the global asymptotic stability of the positive equilibrium is studied. Finally, some numerical simulations are presented to verify our theoretical results. It shows that the system has various spatiotemporal patterns induced by delay.

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Acknowledgements

The work is supported by National Science Foundation of China under Grants 61807006. The work is partially supported by Natural Science Foundation of Jiangsu Province under Grant SBK2020044167, and Jiangsu University Natural Science Foundation Grant No.18KJD110001 and also supported by the Startup Foundation for Introducing Talent of NUIST.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Xuebing Zhang & Qi An

  2. Nanjing Vocational University of Industry Technology, Nanjing, 210000, People’s Republic of China

    Ling Wang

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  1. Xuebing Zhang
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  2. Qi An
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  3. Ling Wang
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Correspondence to Xuebing Zhang.

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Zhang, X., An, Q. & Wang, L. Spatiotemporal dynamics of a delayed diffusive ratio-dependent predator–prey model with fear effect. Nonlinear Dyn 105, 3775–3790 (2021). https://doi.org/10.1007/s11071-021-06780-x

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