Asymptotic behavior of solutions in one predator–prey model with delay

We consider some system of delay differential equations describing the interaction between predator and prey populations and accounting for the age structure of the predator population. Under study are the asymptotic properties of solutions to this system. We establish the estimates that characterize the solution stabilization rate at infinity as well as the estimates for the attraction domains of asymptotically stable equilibrium points. These results base on the use of Lyapunov–Krasovskii functionals.