Journal of Mathematical Biology

, Volume 45, Issue 6, pp 511–548

On spreading speeds and traveling waves for growth and migration models in a periodic habitat

Authors

  • Hans F. Weinberger
    • School of Mathematics, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis, MN 55455, USA. e-mail: hfw@math.umn.edu

DOI: 10.1007/s00285-002-0169-3

Cite this article as:
Weinberger, H. J. Math. Biol. (2002) 45: 511. doi:10.1007/s00285-002-0169-3

Abstract.

 It is shown that the methods previously used by the author [Wei82] and by R. Lui [Lui89] to obtain asymptotic spreading results and sometimes the existence of traveling waves for a discrete-time recursion with a translation invariant order preserving operator can be extended to a recursion with a periodic order preserving operator. The operator can be taken to be the time-one map of a continuous time reaction-diffusion model, or it can be a more general model of time evolution in population genetics or population ecology in a periodic habitat. Methods of estimating the speeds of spreading in various directions will also be presented.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002