Spatio-temporal dynamics for cooperative reaction-diffusion systems with asymptotic annihilation

Abstract

In this paper, we investigate the spatio-temporal dynamics for cooperative random diffusion and nonlocal dispersal systems with time-periodic shifting environment. Under the assumption that the edge of our habitat is shifting and both two limiting systems exhibit asymptotic annihilation, we firstly prove the spreading extinction of solutions. Then we establish the threshold dynamics of time-periodic forced wave via the asymptotic spectral radius, which is well-defined and admits a lower bound determined by an associated Dirichlet boundary value problem. Our analysis is mainly based on the recent theory developed for monotone evolution systems with asymptotic translation invariance.