Global analysis of a three-dimensional delayed Michaelis-Menten chemostat-type models with pulsed input

摘要

In this paper, a new three-dimensional Michaelis-Menten type chemostat model with time delay and pulsed input nutrient concentration is considered. By means of a fixed point in Poincare map for the discrete dynamical system, we obtain a semi-trivial periodic solution, further, we establish the sufficient conditions for the global attractivity of the semi-trivial periodic solution. By use of new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delays are “profitless”. The results are further substantiated by numerical simulation.