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Dynamics of a Predator-Stage Structured Model with Cannibalism, Degenerate Diffusion and Free Boundaries

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Abstract

This paper is concerned with the dynamics of a predator-stage structured model with cannibalism, degenerate diffusion and free boundaries. The existence and uniqueness of the global solution are discussed firstly. Next, we investigate long time behavior of the predators and the prey. Then a spreading–vanishing dichotomy and the criteria are obtained for two cases. The theoretical analyses indicate that: (i) the propagation profile of the free boundary problem is significantly different from that of the corresponding ordinary differential equations; (ii) the transition ratio of two developing forms (cannibalization and natural maturation) from juvenile to adult stage should be sufficiently small so that predators can spread successfully.

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Authors and Affiliations

  1. School of Mathematics and Big Data, Foshan University, Foshan, 528000, People’s Republic of China

    Dawei Zhang & Chufen Wu

  2. School of Mathematics and Data Science, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, People’s Republic of China

    Yun Huang

  3. Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Dawei Zhang & Jianshe Yu

Authors
  1. Dawei Zhang
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  2. Yun Huang
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  3. Chufen Wu
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  4. Jianshe Yu
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Correspondence to Jianshe Yu.

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This work is supported by the Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515110585), the National Natural Science Foundation of China (Nos. 11631005, 11901091, 12071074 and 12101121) and the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT16R16).

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Zhang, D., Huang, Y., Wu, C. et al. Dynamics of a Predator-Stage Structured Model with Cannibalism, Degenerate Diffusion and Free Boundaries. J Geom Anal 33, 86 (2023). https://doi.org/10.1007/s12220-022-01138-0

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  • DOI: https://doi.org/10.1007/s12220-022-01138-0

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