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Interplay between scales in the nonlocal FKPP equation

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  • Piva, G.G.
  • Colombo, E.H.
  • Anteneodo, C.

Abstract

We consider a generalization of the FKPP equation for the evolution of the spatial density of a single-species population where all the terms are nonlocal. That is, the spatial extension of each process (growth, competition and diffusion) is ruled by an influence function, with a characteristic shape and range of action. Our purpose is to investigate the interference between these different components in pattern formation. We show that, while competition is the leading process behind patterns, the other two can act either constructively or destructively. For instance, diffusion that is commonly known to smooth out the concentration field can actually favor pattern formation depending on the shape and range of the dispersal kernel. The results are supported by analytical calculations accompanied by numerical simulations.

Suggested Citation

  • Piva, G.G. & Colombo, E.H. & Anteneodo, C., 2021. "Interplay between scales in the nonlocal FKPP equation," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009632
    DOI: 10.1016/j.chaos.2021.111609
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    References listed on IDEAS

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    1. Cisternas, Jaime & Escaff, Daniel & Clerc, Marcel G. & Lefever, René & Tlidi, Mustapha, 2020. "Gapped vegetation patterns: Crown/root allometry and snaking bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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    4. Alexandre Souto Martinez & Rodrigo Silva Gonzalez & Cesar Augusto Sangaletti Tercariol, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Papers 0803.2635, arXiv.org, revised May 2008.
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    Cited by:

    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. Navidad Maeso, David & Patriarca, Marco & Heinsalu, Els, 2022. "Influence of invasion on natural selection in dispersal-structured populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    3. Piva, G.G. & Anteneodo, C., 2025. "Influence of density-dependent diffusion on pattern formation in a refuge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    4. Pinto-Ramos, D. & Echeverría-Alar, S. & Clerc, M.G. & Tlidi, M., 2022. "Vegetation covers phase separation in inhomogeneous environments," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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