Propagation Dynamics for a Degenerate Delayed System with Nonlocal Dispersal in Periodic Habitats

Abstract

In this paper, we study the existence of spread speeds and periodic traveling waves for a class of space–time periodic and degenerate cooperative systems with nonlocal dispersal and delays. In order to characterize the spread speeds, we first establish the principal eigenvalue theory for linear space–time periodic and degenerate systems with nonlocal dispersal and delays and give some sufficient conditions for the existence of the principal eigenvalue. Then, we prove the existence of a single spreading speed and give the computational formulae of it. Finally, we generalize the monotone iteration scheme combined with the method of sub–super-solutions to prove the existence of the space–time periodic traveling waves.