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

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Abstract

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 λ^* as a threshold, we analyzed the global dynamics of this model. The results showed that the population will go extinct if λ^* < 0, but persist if λ^* > 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.

Keywords

reaction-diffusion / almost periodic / single-species / maturation period / global dynamics

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