Abstract:
For several species of microorganisms, a competition model described by a system of nonlinear differential equations with an infinite distributed delay is considered. The asymptotic stability of the equilibrium point corresponding to the survival of only one species and extinction of the others is studied. Conditions on the initial species population sizes and the initial nutrient concentration are indicated under which the system reaches the equilibrium. Additionally, the stabilization rate is estimated. The results are obtained using a Lyapunov–Krasovskii functional.
Key words:species competition model, chemostat, delay differential equations, infinite distributed delay, equilibrium point, asymptotic stability, estimates for solutions, domain of attraction, Lyapunov–Krasovskii functional.
