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Impacts of prey-taxis and nonconstant mortality on a spatiotemporal predator–prey system

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  • Wu, Daiyong
  • Yang, Youwei
  • Wu, Peng

Abstract

Prey-taxis, which plays an important role in biological control and ecological balance, is the phenomenon that predators shift directly toward regions with the highest density of prey. In this paper, we consider a spatiotemporal predator–prey system involving prey-taxis and nonconstant mortality. By structuring Lyapunov functional, we obtain the global stability of spatially homogeneous steady states. The minimal mortality of predator will determine whether they can survive. In addition, we identify the parameter ranges that spatially homogeneous steady state remains stable or becomes unstable, and discuss steady state bifurcation by choosing prey-taxis coefficient. It is found that a diffusion-induced instability can occur under nonconstant mortality, and prey-taxis can annihilate the spatial patterns induced by diffusion. Numerical simulations illustrate that prey-taxis and nonconstant mortality can result in rich pattern formations including spots pattern, spots–strips pattern, labyrinth pattern, strips-like pattern. It is worth noting that the weak prey-taxis is disadvantageous in terms of the number of two species.

Suggested Citation

  • Wu, Daiyong & Yang, Youwei & Wu, Peng, 2023. "Impacts of prey-taxis and nonconstant mortality on a spatiotemporal predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 283-300.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:283-300
    DOI: 10.1016/j.matcom.2023.01.034
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    References listed on IDEAS

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    1. Guin, Lakshmi Narayan & Baek, Hunki, 2018. "Comparative analysis between prey-dependent and ratio-dependent predator–prey systems relating to patterning phenomenon," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 100-117.
    2. Luo, Demou, 2021. "Global bifurcation for a reaction–diffusion predator–prey model with Holling-II functional response and prey–taxis," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
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