Estimates for solutions in a predator-prey model describing plankton-fish interaction

Abstract

In the paper we consider a system of differential equations with two delays describing plankton--fish interaction. We study stability of the equilibrium point corresponding to the presence of phytoplankton and zooplankton in the system and the absence of fish. In the case of asymptotic stability, we indicate conditions for the initial data under which solutions stabilize to this equilibrium point and establish estimates for solutions characterizing the stabilization rate at infinity. The results are obtained using Lyapunov-Krasovskii functional. The obtained theoretical results can be used for numerical study of behavior of solutions to the considered model.