Global Asymptotics in Some Quasimonotone Reaction-Diffusion Systems with Delays

Both dichotomy and trichotomy on the global asymptotics of some quasimonotone reaction-diffusion systems with delays are established in terms of the principal eigenvalue of linear weakly coupled elliptic systems. Applications to a class of delayed reaction-diffusion models of single species growth and to a reaction-diffusion system with delay, modelling the spread of bacterial infections, are provided.