Pattern formation driven by cross-diffusion in the Klausmeier-Gray-Scott model

Giuseppe Alì, Carmelo Scuro and Isabella Torcicollo

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 555-571

Abstract: Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents. The Klausmeier-Gray-Scott 2D model for semi-arid ecosystems on a sloped terrain is considered with the addition of a nonlinear cross-diffusion term. Pattern formation driven by cross-diffusion is studied in the resulting system. A weakly nonlinear analysis around the critical value of the cross-diffusion is performed, and the asymptotic expansion is validated by numerical solution of the full system.

Keywords: Vegetation patterns; Weakly nonlinear analysis; Turing instability (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:555-571

DOI: 10.1016/j.matcom.2025.06.005

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