Showing papers by "Nanako Shigesada published in 2008"
TL;DR: An idea used by Thieme is extended to show that a class of integro-difference models for a periodically varying habitat has a spreading speed and a formula for it, even when the recruitment function R(u, x) is not nondecreasing in u, so that overcompensation occurs.
Abstract: An idea used by Thieme (J. Math. Biol. 8, 173–187, 1979) is extended to show that a class of integro-difference models for a periodically varying habitat has a spreading speed and a formula for it, even when the recruitment function R(u, x) is not nondecreasing in u, so that overcompensation occurs. Numerical simulations illustrate the behavior of solutions of the recursion whose initial values vanish outside a bounded set.
45 citations
TL;DR: In this paper, it is shown that a trick introduced by H. R. Thieme to study a one-species integral equation model with a non-monotone======.................... operator can be used to show that some multispecies reaction-diffusion systems which are cooperative for small population densities but not for large ones have a spreading====== speed.
Abstract: It is shown that a trick introduced by H. R. Thieme [6] to
study a one-species integral equation model with a nonmonotone
operator can be used to show that some multispecies
reaction-diffusion systems which are cooperative for small
population densities but not for large ones have a spreading
speed. The ideas are explained by considering a model for the
interaction between ungulates and grassland.
19 citations