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Turing patterns in hyperbolic reaction-transport vegetation models with cross-diffusion

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  • Currò, C.
  • Grifò, G.
  • Valenti, G.

Abstract

In this paper, the pattern formation process in arid environments on flat terrains is investigated. In particular, a class of one-dimensional hyperbolic reaction-transport vegetation model with a cross-diffusion term accounting for plant roots’ suction in the soil water diffusion feedback is considered. To characterize the emerging Turing patterns, linear stability analysis on the uniform steady states is first addressed. Then, multiple-scale weakly nonlinear analysis is performed to describe the time evolution of the pattern amplitude close to the stability threshold. Finally, to validate analytical predictions, a modified Klausmeier model which takes also into account the internal competition rate is studied. The effects of the inertial times as well as the cross-diffusion and the internal competition rate are illustrated both analytically and numerically.

Suggested Citation

  • Currò, C. & Grifò, G. & Valenti, G., 2023. "Turing patterns in hyperbolic reaction-transport vegetation models with cross-diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010548
    DOI: 10.1016/j.chaos.2023.114152
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    1. Martinez-Garcia, Ricardo & Cabal, Ciro & Calabrese, Justin M. & Hernández-García, Emilio & Tarnita, Corina E. & López, Cristóbal & Bonachela, Juan A., 2023. "Integrating theory and experiments to link local mechanisms and ecosystem-level consequences of vegetation patterns in drylands," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Wang, Fatao & Yang, Ruizhi, 2023. "Spatial pattern formation driven by the cross-diffusion in a predator–prey model with Holling type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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    4. Ghorai, Santu & Bairagi, Nandadulal, 2022. "Instabilities in hyperbolic reaction–diffusion system with cross diffusion and species-dependent inertia," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
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    7. Ghorai, Santu & Poria, Swarup, 2016. "Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 421-429.
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    1. Consolo, Giancarlo & Curró, Carmela & Grifó, Gabriele & Valenti, Giovanna, 2024. "Stationary and Oscillatory patterned solutions in three-compartment reaction–diffusion systems: Theory and application to dryland ecology," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    2. Grifó, Gabriele & Curró, Carmela & Valenti, Giovanna, 2025. "Heteroclinic connections in a hyperbolic reaction-transport model for excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
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    5. Li, Feiran & Yang, Ruizhi & Liu, Liqin, 2025. "Synergistic effects of feedback regulation and vegetation internal competition on vegetation patterns in semi-arid environments," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).

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