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Spatial dynamics of a predator-prey system with cross diffusion

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  • Wang, Caiyun
  • Qi, Suying

Abstract

In this paper, a spatial predator-prey model with self-defense mechanism that the prey species keep themselves away from the attack of the predator, which leads the existence of the cross diffusion in biological communities, is investigated. Conditions for cross diffusion induced Turing instability are obtained by mathematical analysis. By the numerical simulations, five types of patterns such as hot/cold spots, hot/cold spots-stripes and stripes patterns emerge. Our study suggests that the interactions of self and cross diffusion have great effects on the mechanism for the emergence of complex dynamics in biological systems.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:55-60
    DOI: 10.1016/j.chaos.2017.12.020
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    References listed on IDEAS

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    1. Hu, Jiang-Hong & Xue, Ya-Kui & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2016. "Global dynamics of a predator–prey system modeling by metaphysiological approach," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 369-384.
    2. Li, Li, 2015. "Bifurcation and chaos in a discrete physiological control system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 397-404.
    3. Gui-Quan Sun & Zhen Jin & Yi-Guo Zhao & Quan-Xing Liu & Li Li, 2009. "Spatial Pattern In A Predator-Prey System With Both Self- And Cross-Diffusion," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 71-84.
    4. Sun, Gui-Quan & Jin, Zhen & Liu, Quan-Xing & Li, Li, 2008. "Dynamical complexity of a spatial predator–prey model with migration," Ecological Modelling, Elsevier, vol. 219(1), pages 248-255.
    5. Xing, Yi & Song, Lipeng & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2017. "Assessing reappearance factors of H7N9 avian influenza in China," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 192-204.
    6. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
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    Cited by:

    1. Wang, Henan & Liu, Ping, 2023. "Pattern dynamics of a predator–prey system with cross-diffusion, Allee effect and generalized Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2023. "Qualitative study of cross-diffusion and pattern formation in Leslie–Gower predator–prey model with fear and Allee effects," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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