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Global dynamics of an almost periodic diffusive single-species model with age structure
Electronic Research Archive 2026, 34(4): 2364-2381
Published: 15 April 2026
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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.

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