A time-space periodic population growth model with impulsive birth

This paper is devoted to the study of spatio-temporal dynamics for a time-space periodic population growth model with impulsive birth. We first formulate a discrete-time semiflow by the 1-year solution map, and obtain a threshold-type result for the semiflow with spatially periodic initial data. Then we establish the existence and the computational formulas of the spreading speeds and prove the coincidence of the spreading speeds with the minimal speeds of spatially periodic traveling waves in the monotone case. Further, we investigate the global dynamics of this model in a bounded spatial domain. Finally, we conduct numerical simulations to verify our analytical results and illustrate some interesting findings.