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Bifurcation analysis of a delayed diffusive predator–prey model with spatial memory and toxins

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Abstract

In this paper, we propose a diffusive predator–prey model with two delays, i.e., a spatial memory delay and a toxic effect delay. Initially, we analyze the global existence of the solution of the system. We then analyze the equilibria’s local stability without delays and investigate the Hopf bifurcation induced by one delay. Subsequently, we establish an analytical framework for constructing the stability switching curve in the delay space. Finally, we present numerical simulations to validate the theoretical results and verify the emergence of various spatial patterns in the system.

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Acknowledgements

This work is supported by the National Social Science Fund Youth Project of China [Grant 21CJY040].

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Authors and Affiliations

  1. School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Ming Wu & Hongxing Yao

  2. Faculty of Science, Jinling Institute of Technology, Nanjing, 211169, People’s Republic of China

    Ming Wu

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  1. Ming Wu
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  2. Hongxing Yao
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Correspondence to Hongxing Yao.

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Wu, M., Yao, H. Bifurcation analysis of a delayed diffusive predator–prey model with spatial memory and toxins. Z. Angew. Math. Phys. 75, 25 (2024). https://doi.org/10.1007/s00033-023-02157-9

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  • DOI: https://doi.org/10.1007/s00033-023-02157-9

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