ESTIMATES FOR SOLUTIONS OF A BIOLOGICAL MODEL WITH INFINITE DISTRIBUTED DELAY

A model of competition between several microorganism species described by a system of nonlinear differential equations with infinite distributed delay is considered. The case of asymptotic stability of the equilibrium point corresponding to the survival of only one species and the extinction of all others is studied. The conditions for the initial numbers of species and the initial concentration of the nutrient at which the system reaches an equilibrium state are specified, and estimates of the stabilization rate are established. The results are obtained using the Lyapunov–Krasovskii functional.