ncts

In this talk, we consider the large time behavior for two components reaction-diffusion systems of prey-predator type in a time varying environment. These time variations are assumed to enjoy an averaging property, including time periodicity and almost periodicity as special cases. We are interested in situations where two species can co-invade an empty space. We derive some estimates between the prey and the predator densities. These estimates enable us to compare the solutions of the prey-predator system with those of a KPP-type scalar equation on suitable spatial temporal domains. By the similar idea, we can also study the spreading speeds for a non-autonomous prey-predator system on a lattice with a discrete convolution diffusion operator. We also provide a new approach inspired by persistence theory to study spreading speeds for nonlocal diffusion KPP equations. This talk is based on joint works with Arnaud Ducrot.