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Analysis of Integrodifference Equations with a Separable Dispersal Kernel

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Abstract

Integrodifference equations are a class of infinite-dimensional dynamical systems in discrete time that have recently received great attention as mathematical models of population dynamics in spatial ecology. The dispersal of individuals between generations is described by a ‘dispersal kernel’, a probability density function for the distance that an individual moves within a season. Previous authors recognized that the dynamics are reduced to a finite-dimensional problem when the dispersal kernel is separable. We prove some open questions from their work on the dynamics of a single population and then extend the idea to investigate the dynamics of two spatially distributed species in (i) a competitive relation, and (ii) a predator-prey relation. In all cases, we discuss how the dynamics of the population(s) depend on the amount of suitable space that is available to them. We find a number of bifurcations, such as period-doubling sequences and Naimark-Sacker bifurcations, which we illustrate through simulations.

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Author notes

  1. Jason Bramburger

    Present address: Division of Applied Mathematics, Brown University, Providence, RI, 02906, USA

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N8G1, Canada

    Jason Bramburger

  2. Department of Mathematics and Statistics and Department of Biology, University of Ottawa, Ottawa, ON, K1N8G1, Canada

    Frithjof Lutscher

Authors
  1. Jason Bramburger
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  2. Frithjof Lutscher
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Correspondence to Frithjof Lutscher.

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Bramburger, J., Lutscher, F. Analysis of Integrodifference Equations with a Separable Dispersal Kernel. Acta Appl Math 161, 127–151 (2019). https://doi.org/10.1007/s10440-018-0207-9

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  • DOI: https://doi.org/10.1007/s10440-018-0207-9

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