On spreading speeds and traveling waves for growth and migration models in a periodic habitat.
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.
Weinberger
Hans F
HF
School of Mathematics, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis 55455, USA. hfw@math.umn.edu
D000818:Animals; D017753:Ecosystem; D004641:Emigration and Immigration; D004777:Environment; D005828:Genetics, Population; D008957:Models, Genetic; D011157:Population Dynamics