Dynamic analysis of a prey–predator model with state-dependent control strategy and square root response function

In this work, a prey-predator model with square root response function under a state-dependent impulse is proposed. Firstly, according to the differential equation geometry theory and the method of successor function, the existence, uniqueness and attractiveness of the order-1 periodic solution are analyzed. Then the stability of the order-1 periodic solution is discussed by the Poincaré criterion for impulsive differential equations. Finally, we show a specific example and carry out numerical simulations to verify the theoretical results.