IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip2s0960077921009632.html
   My bibliography  Save this article

Interplay between scales in the nonlocal FKPP equation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009632
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.111609?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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).
    2. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    3. Souto Martinez, Alexandre & Silva González, Rodrigo & Lauri Espíndola, Aquino, 2009. "Generalized exponential function and discrete growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2922-2930.
    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.
    5. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Destefano, Natália & Martinez, Alexandre Souto, 2011. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1763-1772.
    2. Cabella, Brenno Caetano Troca & Ribeiro, Fabiano & Martinez, Alexandre Souto, 2012. "Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1281-1286.
    3. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    4. Natalia Destefano & Alexandre Souto Martinez, 2010. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Papers 1010.5648, arXiv.org, revised May 2011.
    5. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    6. Moriguchi, Kai, 2018. "An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1150-1163.
    7. Barberis, L. & Condat, C.A. & Román, P., 2011. "Vector growth universalities," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1100-1105.
    8. Rivera-Castro, Miguel A. & Miranda, José G.V. & Borges, Ernesto P. & Cajueiro, Daniel O. & Andrade, Roberto F.S., 2012. "A top–bottom price approach to understanding financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1489-1496.
    9. Takahashi, Taiki, 2010. "A social discounting model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3600-3603.
    10. James J Elser & Timothy J Elser & Stephen R Carpenter & William A Brock, 2014. "Regime Shift in Fertilizer Commodities Indicates More Turbulence Ahead for Food Security," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-7, May.
    11. Darrell Jiajie Tay & Chung-I Chou & Sai-Ping Li & Shang You Tee & Siew Ann Cheong, 2016. "Bubbles Are Departures from Equilibrium Housing Markets: Evidence from Singapore and Taiwan," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-13, November.
    12. Dur, Gaël & Won, Eun-Ji & Han, Jeonghoon & Lee, Jae-Seong & Souissi, Sami, 2021. "An individual-based model for evaluating post-exposure effects of UV-B radiation on zooplankton reproduction," Ecological Modelling, Elsevier, vol. 441(C).
    13. Martin Lindegren & Vasilis Dakos & Joachim P Gröger & Anna Gårdmark & Georgs Kornilovs & Saskia A Otto & Christian Möllmann, 2012. "Early Detection of Ecosystem Regime Shifts: A Multiple Method Evaluation for Management Application," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    14. Simon DeDeo, 2016. "Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions," Future Internet, MDPI, vol. 8(3), pages 1-23, July.
    15. Quentin Remy & Julius Hohlfeld & Maxime Vergès & Yann Le Guen & Jon Gorchon & Grégory Malinowski & Stéphane Mangin & Michel Hehn, 2023. "Accelerating ultrafast magnetization reversal by non-local spin transfer," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    16. Corsi, Fulvio & Lillo, Fabrizio & Pirino, Davide & Trapin, Luca, 2018. "Measuring the propagation of financial distress with Granger-causality tail risk networks," Journal of Financial Stability, Elsevier, vol. 38(C), pages 18-36.
    17. Florian Wagener, 2013. "Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict," Computational Management Science, Springer, vol. 10(4), pages 423-450, December.
    18. Palola, Pirta & Bailey, Richard & Wedding, Lisa, 2022. "A novel framework to operationalise value-pluralism in environmental valuation: Environmental value functions," Ecological Economics, Elsevier, vol. 193(C).
    19. Maeno, Yoshiharu, 2011. "Discovery of a missing disease spreader," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3412-3426.
    20. Tousheng Huang & Huayong Zhang & Zhao Liu & Ge Pan & Xiumin Zhang & Zichun Gao, 2019. "Theoretical Study on Self-Organization of Vegetation Patterns Triggered by Water Resource in Deposited Sediment Layer," Complexity, Hindawi, vol. 2019, pages 1-11, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009632. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.