Globally exponentially stable periodic solution in a general delayed predator-prey model under discontinuous prey control strategy

This paper studies the solution behaviour of a general delayed predator-prey model with discontinuous prey control strategy. The positiveness and boundeness of the solution of the system is firstly investigated using the comparison theorem. Then the sufficient conditions are derived for the existence of positive periodic solutions using the differential inclusion theory and the topological degree theory. Furthermore, the positive periodic solution is proved to be globally exponentially stable by employing the generalized Lyapunov approach. The global finite-time convergence is also discussed for the system state. Finally, the numerical simulations of four examples are given to validate the correctness of the theoretical results