Abstract
An age-structured juvenile-adult model with impulsive harvesting is developed on a periodically evolving domain. The principal eigenvalue is firstly defined by Krein–Rutman theorem on a Banach space involving impulse and its properties are explicitly discussed. Moreover, sufficient conditions for the solution to persist or extinct are presented by comparison principle with impulse. The final numerical simulations are carried out to verify our analytical findings. Our results imply that harvesting pulse can make individuals from persistence to struggle to survive, or from extinction to rapidly extinction. Moreover, small rate of regional evolution are detrimental to species persistence, that is, small evolutional rate turns individuals from persistence to extinction.
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