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Effects of gradual spatial variation in resources on population extinction: Analytic calculations for abrupt transitions

Author

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  • Kumar, Niraj
  • Kenkre, V.M.

Abstract

We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations. The result we obtain helps in the understanding of the onset of abrupt transitions leading to the extinction of biological populations. The result is expressed in terms of Airy functions and sheds light on the behavior of bacteria in a Petri dish as well as of large animals such as rodents moving over a landscape.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:2:p:257-262
    DOI: 10.1016/j.physa.2010.09.026
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    Cited by:

    1. 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.
    2. 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.
    3. 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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