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How do seasonal successions influence the propagation dynamics of anage-structured invasive species? We investigate this problem by considering thescenario that the offsprings are reproduced in spring and then reach maturationin fall within the same year. For this purpose, a reaction-diffusion system isproposed, with yearly periodic time delay and spatially nonlocal responsecaused by the periodic developmental process. By appealing to the recentlydeveloped dynamical system theories, we obtain the invasion speed $c^*$ and itscoincidence with the minimal speed of time periodic traveling waves. Thecharacterizations of $c^*$ suggest that (i) time delay decreases the speed andits periodicity may further do so; (ii) the optimal time to slow down theinvasion is the season without juveniles; (iii) the speed increases to infinitywith the same order as the square root of the diffusion rate.

seasonal influence on age-structured invasive species with yearly generation