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Discrete-time travelling waves: Ecological examples

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Abstract

Integrodifference equations are discrete-time models that possess many of the attributes of continuous-time reaction-diffusion equations. They arise naturally in population biology as models for organisms with discrete nonoverlapping generations and well-defined growth and dispersal stages. I examined the varied travelling waves that arise in some simple ecologically-interesting integrodifference equations. For a scalar equation with compensatory growth, I observed only simple travelling waves. For carefully chosen redistribution kernels, one may derive the speed and approximate the shape of the observed waveforms. A model with overcompensation exhibited flip bifurcations and travelling cycles in addition to simple travelling waves. Finally, a simple predator-prey system possessed periodic wave trains and a variety of travelling waves.

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  1. Department of Applied Mathematics, University of Washington, 98195, Seattle, WA, USA

    Mark Kot

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Kot, M. Discrete-time travelling waves: Ecological examples. J. Math. Biol. 30, 413–436 (1992). https://doi.org/10.1007/BF00173295

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