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Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis

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Abstract

This paper concerns the reaction–diffusion systems modeling the population dynamics of two predators and one prey with nonlinear prey-taxis. We first investigate the global existence and boundedness of the unique classical solution for the general model. Then, we study the global stabilities of nonnegative spatially homogeneous equilibria for an explicit system with type I functional responses and density-dependent death rates for the predators and logistic growth for the prey. Moreover, the convergence rates are also established.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Jianping Wang & Mingxin Wang

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  1. Jianping Wang
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  2. Mingxin Wang
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Correspondence to Mingxin Wang.

Additional information

This work was supported by NSFC Grants 11771110 and 11371113.

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Wang, J., Wang, M. Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis. Z. Angew. Math. Phys. 69, 63 (2018). https://doi.org/10.1007/s00033-018-0960-7

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  • DOI: https://doi.org/10.1007/s00033-018-0960-7

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