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Complex Dynamics in a General Diffusive Predator–Prey Model with Predator Maturation Delay

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Abstract

We formulate and analyze a general diffusive predator–prey system with predator maturation delay. Global asymptotic stability of the predator-free equilibrium and uniform persistence results are obtained under different conditions on model parameters. We then use Leray–Schauder degree theory to establish the existence of the spatial heterogeneous steady state. Moreover, we prove the global existence of nonconstant positive steady states bifurcated from the positive constant steady state. Taking the time delay as the bifurcation parameter, we conduct local and global Hopf bifurcation analysis and prove the boundedness of global Hopf branches. Rigorous analyses for global Hopf bifurcation and branches are challenging but important in understanding global transitions of dynamics.

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Acknowledgements

H. Shu was partially supported by the National Natural Science Foundation of China (11971285) and the Fundamental Research Funds for the Central Universities (GK201902005). H. Wang was partially supported by the Natural Sciences and Engineering Research Council of Canada (Discovery Grant RGPIN-2020-03911 and Accelerator Grant RGPAS-2020-00090).

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Authors and Affiliations

  1. School of Mathematical Sciences, Tongji University, Shanghai, 200092, People’s Republic of China

    Wanxiao Xu & Zheng Tang

  2. School of Mathematics and Statistics, Shaanxi Normal University, **’an, 710062, People’s Republic of China

    Hongying Shu

  3. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada

    Hao Wang

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  1. Wanxiao Xu
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  2. Hongying Shu
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  3. Zheng Tang
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  4. Hao Wang
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Correspondence to Hongying Shu.

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Xu, W., Shu, H., Tang, Z. et al. Complex Dynamics in a General Diffusive Predator–Prey Model with Predator Maturation Delay. J Dyn Diff Equat 36, 1879–1904 (2024). https://doi.org/10.1007/s10884-022-10176-9

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  • DOI: https://doi.org/10.1007/s10884-022-10176-9

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