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Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System

Author

Listed:
  • Ying Yu

    (School of Mathematical Science, Yangzhou University, Yangzhou 225002, China)

  • Yahui Chen

    (School of Mathematical Science, Yangzhou University, Yangzhou 225002, China)

  • You Zhou

    (School of Mathematical Science, Yangzhou University, Yangzhou 225002, China)

Abstract

This paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore a unique positive equilibrium solution of the system that is globally asymptotically stable. Additionally, we show that this equilibrium solution remains locally linearly stable, even in the presence of diffusion. This means that the system does not follow classical Turing instability. However, it becomes linearly unstable only when cross-diffusion also plays a role in the system, which is called a cross-diffusion-induced instability. The corresponding numerical simulations are also demonstrated and we obtain the spatial patterns.

Suggested Citation

  • Ying Yu & Yahui Chen & You Zhou, 2023. "Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System," Mathematics, MDPI, vol. 11(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2411-:d:1153334
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    References listed on IDEAS

    as
    1. Meng Zhu & Jing Li & Xinze Lian, 2022. "Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    2. Elettreby, M.F., 2009. "Two-prey one-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2018-2027.
    3. Dhariwal, Gaurav & Jüngel, Ansgar & Zamponi, Nicola, 2019. "Global martingale solutions for a stochastic population cross-diffusion system," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3792-3820.
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