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Predator-taxis creates spatial pattern of a predator-prey model

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  • Chen, Mengxin
  • Zheng, Qianqian

Abstract

In this paper, we investigate the spatial pattern formation to a predator-prey model with the predator-taxis under the homogeneous zero-flux boundary conditions. Firstly, we employ the predator-taxis coefficient as the potential critical value of the Turing bifurcation to perform its role in forming the spatial pattern. One finds that there are multiple thresholds of the Turing bifurcation. Hereafter, we focus on the direction of the Turing bifurcation. To this end, the technique of the weakly nonlinear analysis is employed to deduce the amplitude equation near the threshold of the Turing bifurcation in one-dimensional space. It is found that the predator-taxis can create the subcritical or the supercritical Turing bifurcation. Finally, numerical experiments check the theoretical analysis well and obtain the spatial patterns with the different predator-taxis coefficients.

Suggested Citation

  • Chen, Mengxin & Zheng, Qianqian, 2022. "Predator-taxis creates spatial pattern of a predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005422
    DOI: 10.1016/j.chaos.2022.112332
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    References listed on IDEAS

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    1. Chen, Mengxin & Wu, Ranchao & Liu, Hongxia & Fu, Xiaoxue, 2021. "Spatiotemporal complexity in a Leslie-Gower type predator-prey model near Turing-Hopf point," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Chen, Mengxin & Wu, Ranchao & Chen, Liping, 2020. "Spatiotemporal patterns induced by Turing and Turing-Hopf bifurcations in a predator-prey system," Applied Mathematics and Computation, Elsevier, vol. 380(C).
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    Cited by:

    1. Chen, Mengxin & Zheng, Qianqian, 2023. "Steady state bifurcation of a population model with chemotaxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    2. Chen, Mengxin & Srivastava, Hari Mohan, 2023. "Stability of bifurcating solution of a predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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