Dynamics of a delayed stage-structured model with impulsive harvesting and diffusion

Abstract

Based on the predator–prey system with delayed stage-structured for preys and impulsive harvesting and impulsive diffusion for predator, an impulsive delayed differential equation to model the process of periodic harvesting and impulsive diffusion at different fixed moments is proposed and investigated. In this model, patches are created by two different prey populations and each prey population is confined to a particular patch while the predator population can impulsively diffuse between two patches. By using comparison theorem of impulsive delayed differential equation and some analysis techniques, sufficient conditions ensuring the existence of preys-extinction periodic solution and the permanence of the system are established. Our analysis reveals that low birth rates of immature preys, high death rates of immature and mature preys, long maturation time of immature preys to mature preys and large preys’ captured rates are the sufficient condition for the preys-extinction. On the contrary, if we largen the birth rates of immature preys, or decrease the death rates of immature and mature preys, or shorten the maturation time of immature preys or decrease the preys’ captured rates, then the system can become permanent under proper predational strategies. These also show that it is feasible to keep the sustainable development of the ecosystem by controlling the critical ecological parameters. Numerical simulations with hypothetical set of parameter values are carried out to consolidate the analytic findings.