Periodic solution of a general state-dependent predator-prey model with harvesting

This paper investigates a general state-dependent predator-prey model incorporating impulsive harvesting on predators. By leveraging geometric theory of differential equations and successor function methods, we establish the existence of the order-1 periodic solution. Specifically, under the condition where the unique positive equilibrium exhibits unstable focus dynamics, we prove the existence of an order-1 periodic solution that is strictly contained within the continuous system's limit cycle. Furthermore, the necessary condition for the orbital stability of the order-1 periodic solution is depicted by employing the analogue of Poincaré criterion. Finally, a specific model is provided to exemplify the main results obtained from the general impulse system.