Journal of Mathematical Biology

, Volume 45, Issue 6, pp 511–548 | Cite as

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

  • Hans F. Weinberger


 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.


Time Evolution General Model Population Genetic Continuous Time Population Ecology 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Hans F. Weinberger
    • 1
  1. 1.School of Mathematics, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis, MN 55455, USA. e-mail: hfw@math.umn.eduUS

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