Spatial pattern formation induced by cross-diffusion in a mussel–algae system

Gaihui Guo, Huifeng Shen, Xiaoyi Yang and Sajad Jafari

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: This paper explores Turing-pattern formation in a mussel–algae system with cross-diffusion. We establish conditions for Turing instability, and derive amplitude equations near the Turing threshold. From a mathematical perspective, our analysis demonstrates that the entire range of pattern formation in the system is determined by two key parameters: the cross-diffusion coefficient d21 and the predator mortality rate β. Theoretical and numerical studies reveal complex pattern formation, including spot patterns, stripe patterns, and spot–stripe patterns, as these control parameters are varied. To validate our theoretical findings, a series of numerical simulations are performed, specifically focusing on the diverse patterns near the critical Turing bifurcation point and the significant influence of d21 and β on the spatial distribution of the two species.

Keywords: Mussel–algae model; Cross-diffusion; Amplitude equation; Pattern formations (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926007769

DOI: 10.1016/j.chaos.2026.118635

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