Spatial stochastic predator-prey models

Volume 80 / 2008

Mauro Mobilia, Ivan T. Georgiev, Uwe C. Täuber Banach Center Publications 80 (2008), 253-257 MSC: Primary 92D25; Secondary 82C26, 82C31. DOI: 10.4064/bc80-0-16

Abstract

We consider a broad class of stochastic lattice predator-prey models whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the deterministic rate equations, on the properties of the stochastic models. Here, we outline the robust scenario obeyed by most of the lattice predator-prey models with an interaction à la Lotka-Volterra. We also show how a drastically different behavior can emerge as the result of a subtle interplay between long-range interactions and a nearest-neighbor exchange process.

Authors

  • Mauro MobiliaArnold Sommerfeld Center for Theoretical Physics and Center for NanoScience
    Department of Physics, Ludwig-Maximilians-Universität München
    D-80333 München, Germany
    and
    Department of Physics and Center for Stochastic Processes in Science and Engineering
    Virginia Polytechnic Institute and State University
    Blacksburg
    Virginia 24061-0435, U.S.A.
    e-mail
  • Ivan T. GeorgievDepartment of Physics and Center for Stochastic Processes in Science and Engineering
    Virginia Polytechnic Institute and State University
    Blacksburg
    Virginia 24061-0435, U.S.A.
    e-mail
  • Uwe C. TäuberDepartment of Physics and Center for Stochastic Processes in Science and Engineering
    Virginia Polytechnic Institute and State University
    Blacksburg
    Virginia 24061-0435, U.S.A.
    e-mail

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