Estimates of solutions in the model of interaction of populations with several delays

We consider a system of differential equations with several delays, which describes the interaction of $n$ species of microorganisms. We obtain sufficient conditions for the asymptotic stability of a nontrivial equilibrium state corresponding to the partial survival of populations. We establish estimates of solutions that characterize the rate of stabilization at infinity and indicate estimates of the attraction set of a given equilibrium state. The results are obtained by using the modified Lyapunov–Krasovsky functional.