Journal of Mathematical Biology

, Volume 30, Issue 4, pp 413–436

Discrete-time travelling waves: Ecological examples

  • Mark Kot

DOI: 10.1007/BF00173295

Cite this article as:
Kot, M. J. Math. Biol. (1992) 30: 413. doi:10.1007/BF00173295


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.

Key words

Travelling waves Integrodifferenceequations Bifurcations Diffusion Ecology 

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Mark Kot
    • 1
  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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