Sharp spatiotemporal patterns in the diffusive time-periodic logistic equation

To reveal the complex influence of heterogeneous environment on population systems, we examine the asymptotic profile (as ϵ → 0) of the positive solution to the perturbed periodic logistic equation... We show that the temporal degeneracy of 'b' induces sharp spatiotemporal patterns of the solution only when spatial degeneracy also exists; but in sharp contrast, whether or not temporal degeneracy appears in 'b', the spatial degeneracy always induces sharp spatiotemporal patterns, though they differ significantly according to whether temporal degeneracy is also present.