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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 12 July 2001 / Revised version: 19 July 2002 / Published online: 17 October 2002
Mathematics Subject Classification (2000): 92D40, 92D25, 35K55, 35K57, 35B40
Keywords or phrases: Periodic – Spreading speed – Traveling wave
Rights and permissions
About this article
Cite this article
Weinberger, H. On spreading speeds and traveling waves for growth and migration models in a periodic habitat. J. Math. Biol. 45, 511–548 (2002). https://doi.org/10.1007/s00285-002-0169-3
Issue Date:
DOI: https://doi.org/10.1007/s00285-002-0169-3