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Pattern dynamics of a Lotka-Volterra model with taxis mechanism

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  • Chen, Mengxin

Abstract

This paper deals with the Turing bifurcation and pattern dynamics of a Lotka-Volterra model with the predator-taxis and the homogeneous no-flux boundary conditions. To investigate the pattern dynamics, we first give the occurrence conditions of the Turing bifurcation. It is found that there is no Turing bifurcation when predator-taxis disappears, while the Turing bifurcation occurs as predator-taxis is presented. Next, we establish the amplitude equation by virtue of weakly nonlinear analysis. Our theoretical result suggests the Lotka-Volterra model admits the supercritical or subcritical Turing bifurcation. In this manner, we can determine the stability of the bifurcating solution. Finally, some numerical simulation results verify the validity of the theoretical analysis. The stripe pattern, the mixed patterns, and wave patterns are performed. Interestingly, the stable stripe patterns will be broken and become wave patterns when the predator-taxis parameter is far from the Turing bifurcation critical point.

Suggested Citation

  • Chen, Mengxin, 2025. "Pattern dynamics of a Lotka-Volterra model with taxis mechanism," Applied Mathematics and Computation, Elsevier, vol. 484(C).
    • Handle: RePEc:eee:apmaco:v:484:y:2025:i:c:s0096300324004788
    DOI: 10.1016/j.amc.2024.129017
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    References listed on IDEAS

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    1. Matsumoto, Akio & Szidarovszky, Ferenc, 2020. "Stability switching curves in a Lotka–Volterra competition system with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 422-438.
    2. Chen, Mengxin & Ham, Seokjun & Choi, Yongho & Kim, Hyundong & Kim, Junseok, 2023. "Pattern dynamics of a harvested predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Ke, Yue & Zhu, Linhe & Wu, Peng & Shi, Lei, 2022. "Dynamics of a reaction-diffusion rumor propagation model with non-smooth control," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    4. 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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