Global dynamics of an almost periodic diffusive single-species model with age structure

To understand the significant roles that seasonal variations and diffusion play in population growth, we proposed and investigated an almost periodic reaction-diffusion model incorporating age structure for a single species. The model was formulated as a reaction-diffusion system with a nonlocal term. Using the principal Lyapunov exponent ${\lambda }^{\ast }$ as a threshold, we analyzed the global dynamics of this model. The results showed that the population will go extinct if ${\lambda }^{\ast }<0$, but persist if ${\lambda }^{\ast }>0$. We further established the existence of a globally attractive almost periodic solution when the population was uniformly persistent in a monotone case. The Nicholson blowflies model was investigated by means of numerical simulations, and the dependence of population development on maturation period, diffusion rate, and spatial environment was discussed.