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Turing instability of a discrete competitive single diffusion-driven Lotka–Volterra model

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  • Wen, Mingyao
  • Zhang, Guang
  • Yan, Yubin

Abstract

This paper develops a discrete competitive Lotka–Volterra system with single diffusion under Neumann boundary conditions. It establishes the conditions for Turing instability and identifies the precise Turing bifurcation when the diffusion coefficient is used as a bifurcation parameter. Within Turing unstable regions, a variety of Turing patterns are explored via numerical simulations, encompassing lattice, nematode, auspicious cloud, spiral wave, polygon, and stripe patterns, as well as their combinations. The periodicity and complexity of these patterns are verified through bifurcation simulations, Lyapunov exponent analysis, trajectory or phase diagrams. These methods are also applicable to other single diffusion systems, including partial dissipation systems.

Suggested Citation

  • Wen, Mingyao & Zhang, Guang & Yan, Yubin, 2025. "Turing instability of a discrete competitive single diffusion-driven Lotka–Volterra model," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001596
    DOI: 10.1016/j.chaos.2025.116146
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    References listed on IDEAS

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    1. Zhang, Guang & Zhang, Ruixuan & Yan, Yubin, 2020. "The diffusion-driven instability and complexity for a single-handed discrete Fisher equation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
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