Dynamic Analysis of an Instantaneous/Non‐Instantaneous Unilateral Diffusion Prey–Predator Model With Impulsive Control Strategy

ABSTRACT In this paper, we propose and study an instantaneous/non‐instantaneous unilateral diffusion predator–prey model with impulsive chemical and biological control strategies. Using the theory and the comparison theorem of impulsive differential equations, we obtain the sufficient conditions for the local asymptotic stability and the global asymptotic stability of the prey‐free periodic solution. Then, we prove the permanence of the system and obtain a sufficient condition for the permanence of the system. Finally, some numerical simulations are provided to verify the accuracy of our theoretical results and to further explore some complex dynamical behaviors of the system. These results provide a theoretical basis for coordinating the relationship between chemical control and biological control.