Chemostats with random inputs and wall growth

Abstract

Chemostat refers to a laboratory device used for growing microorganisms in a cultured environment, and has been regarded as an idealization of nature to study competition modeling of mathematical biology. The simple form of chemostat model assumes that the availability of nutrient and its supply rate are both fixed. In addition the tendency of microorganism to adhere to surfaces is neglected by assuming the flow rate is fast enough. However, these assumptions largely limit the applicability of chemostat models to realistic competition systems. In this paper, we relax these assumptions and study the chemostat models with random nutrient supplying rate or random input nutrient concentration, with or without wall growth. This leads the models to random dynamical systems and requires the concept of random attractors developed in the theory of random dynamical systems. Our results include existence of uniformly bounded non-negative solutions, existence of random attractors and geometric details of random attractors for different value of parameters.