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.
Pattern formation driven by cross-diffusion in the Klausmeier-Gray-Scott model
Torcicollo I.
2026
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.File in questo prodotto:
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Descrizione: Pattern formation
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