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

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  • Alì, Giuseppe
  • Scuro, Carmelo
  • Torcicollo, Isabella

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.

Suggested Citation

  • Alì, Giuseppe & Scuro, Carmelo & Torcicollo, Isabella, 2026. "Pattern formation driven by cross-diffusion in the Klausmeier-Gray-Scott model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 555-571.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:555-571
    DOI: 10.1016/j.matcom.2025.06.005
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