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

Hans F. Weinberger

Research output: Contribution to journalArticlepeer-review

271 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)511-548
Number of pages38
JournalJournal of Mathematical Biology
Volume45
Issue number6
DOIs
StatePublished - Dec 1 2002

Keywords

  • Periodic
  • Spreading speed
  • Traveling wave

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