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Isolation effects in a system of two mutually communicating identical patches

Author

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  • Pamplona da Silva, D.J.
  • Villar, R.P.
  • Ramos, L.C.

Abstract

Starting from the Fisher–Kolmogorov–Petrovskii–Piskunov equation (FKPP) we model the dynamic of a diffusive system with two mutually communicating identical patches and isolated of the remaining matrix. For this system we find the minimal size of each fragment in the explicit form and compare with the explicit results for similar problems found in the literature. From this comparison emerges an unexpected result that for a same set of the parameters, the isolated system studied in this work with size L, can be better or worst than the non isolated systems with the same size L, uniquely depending on the parameter a0 (internal conditions of the patches). Due to the fact that this result is unexpected we propose an experimental verification.

Suggested Citation

  • Pamplona da Silva, D.J. & Villar, R.P. & Ramos, L.C., 2017. "Isolation effects in a system of two mutually communicating identical patches," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 494-499.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:494-499
    DOI: 10.1016/j.amc.2017.08.003
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    References listed on IDEAS

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    1. Kumar, Niraj & Kenkre, V.M., 2011. "Effects of gradual spatial variation in resources on population extinction: Analytic calculations for abrupt transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 257-262.
    2. Sergio Beraldo & Robert Sugden, 2010. "The emergence of reciprocally beneficial cooperation," ICER Working Papers 18-2010, ICER - International Centre for Economic Research.
    3. Pamplona da Silva, D.J. & Kraenkel, R.A., 2012. "Population persistence in weakly-coupled sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 142-146.
    4. Kraenkel, R.A. & da Silva, D.J. Pamplona, 2010. "Stochastic Skellam model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 60-66.
    5. Sergio Beraldo & Robert Sugden, 2016. "The emergence of reciprocally beneficial cooperation," Theory and Decision, Springer, vol. 80(4), pages 501-521, April.
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    Cited by:

    1. Pamplona da Silva, D.J., 2018. "Crossing-effect in non-isolated and non-symmetric systems of patches," Ecological Modelling, Elsevier, vol. 384(C), pages 168-172.

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