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

Mingyao Wen, Guang Zhang and Yubin Yan

Chaos, Solitons & Fractals, 2025, vol. 194, issue C

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.

Keywords: Single diffusion; Turing pattern; Bifurcation; Periodicity (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001596

DOI: 10.1016/j.chaos.2025.116146

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