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Complex Dynamical Behavior of Holling–Tanner Predator‐Prey Model with Cross‐Diffusion

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  • Caiyun Wang
  • Yongyong Pei
  • Yaqun Niu
  • Ruiqiang He

Abstract

Spatial predator‐prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator‐prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black‐eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross‐diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross‐diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology.

Suggested Citation

  • Caiyun Wang & Yongyong Pei & Yaqun Niu & Ruiqiang He, 2022. "Complex Dynamical Behavior of Holling–Tanner Predator‐Prey Model with Cross‐Diffusion," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:8238384
    DOI: 10.1155/2022/8238384
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    References listed on IDEAS

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    1. Duan, Moran & Chang, Lili & Jin, Zhen, 2019. "Turing patterns of an SI epidemic model with cross-diffusion on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    2. Wang, Caiyun & Qi, Suying, 2018. "Spatial dynamics of a predator-prey system with cross diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 55-60.
    3. Li, Jing & Jin, Zhen & Sun, Gui-Quan, 2016. "Periodic solutions of a spatiotemporal predator-prey system with additional food," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 350-359.
    4. repec:plo:pone00:0150503 is not listed on IDEAS
    5. Guo, Zun-Guang & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen & Li, Li & Li, Can, 2020. "Spatial dynamics of an epidemic model with nonlocal infection," Applied Mathematics and Computation, Elsevier, vol. 377(C).
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