In this talk, we introduce a seasonally interactive model between closed season and open season based on Michaelis-Menten type harvesting. Assume that the single species grows at the well-known logistic rate during the closed season, and is harvested by Michaelis-Menten type function rate in the open season. By defining two length thresholds of the closed season, we provide a comprehensive description of the dynamics of the model, which includes the existence and the number of periodic solutions, as well as the stability of both the origin and periodic solutions. Numerical examples are carried out to support these theoretical results. Brief conclusions and discussions on our findings are also provided.

This is a joint work with Yunfeng Liu，Shigui Ruan and Jianshe Yu.