Impulsive control to a periodic plant-pest-natural enemy model in a patchy environment

To achieve better economic balance, biological control (e.g. releasing natural enemies) and chemical control (e.g. spraying pesticides) are often implemented together to combat agricultural pests. These control measures are typically applied at different times. Taking these factors into account, we propose a time-periodic plant-pest-natural enemy model in a patchy environment, and investigate key mathematical properties of the model, including the existence of a ‘pest-free’ periodic solution, its local stability, and the persistence of the system. Furthermore, we derive sufficient conditions ensuring the global asymptotic stability of the pest-free periodic solution. Finally, we present two illustrative examples, along with numerical simulations, to validate the effectiveness of our theoretical conclusions.