A novel method for analyzing the stability of periodic solution of impulsive state feedback model

The complex dynamics on the single population model with impulsively unilateral diffusion between two patches was studied in a theoretical way. The existence, uniqueness and stability of an order-1 periodic solution was investigated for state-dependent impulsively differential equations. The sufficient conditions for the existence and stability of positive periodic solution were obtained using the Poincare map by comparison with the analysis for limit cycles of continuous systems, which was different from the analogue of Poincare criterion. Meanwhile, the uniqueness of periodic solution was proofed by the monotone of successor function.