PERIODIC SOLUTIONS AND STABILITY OF A DISCRETE MOSQUITO POPULATION MODEL WITH PERIODIC PARAMETERS

. In this paper, we establish and study a discrete mosquito population model with periodic parameters that takes into account the seasonal variation of environments. We are mainly interested in finding a positive periodic solution that is asymptotically stable and attracts all positive solutions. The existence, uniqueness, and stability of periodic solutions of the model are investigated. We show that the instability of the origin implies that the model has a unique asymptotically stable positive periodic solution and attracts all positive solutions and that the local stability of the origin implies its global asymptotic stability. We also give a necessary and sufficient condition for the origin to be stable. Numerical examples are provided to illustrate our theoretical results.