On spreading speeds and traveling waves for growth and migration models in a periodic habitat
- Cite this article as:
- Weinberger, H. J. Math. Biol. (2002) 45: 511. doi:10.1007/s00285-002-0169-3
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.