Dynamical Analysis of a Stochastic Multispecies Turbidostat Model

Yu Mu,Zuxiong Li,Huili Xiang,Hailing Wang

doi:10.1155/2019/4681205

Abstract

A stochastic turbidostat system in which the dilution rate is subject to white noise is investigated in this paper. First of all, sufficient conditions of the competitive exclusion among microorganisms are obtained by employing the techniques of stochastic analysis. Furthermore, the results demonstrate that the competition among microorganisms and stochastic disturbance will affect the dynamical behaviors of microorganisms. Finally, the theoretical results obtained in this contribution are illustrated by numerical simulations.

Highlights

The chemostat and turbidostat, two types of devices for continuous cultivation of microorganism, have been utilized to analyze population dynamics
The results demonstrate that the competition among microorganisms and stochastic disturbance will affect the dynamical behaviors of microorganisms
There exist some drawbacks in chemostat model with a constant dilution rate, such as the waste of substrate and higher viscosity caused by the mass transfer efficiency

Summary

Introduction

The chemostat and turbidostat, two types of devices for continuous cultivation of microorganism, have been utilized to analyze population dynamics. Wolkowicz et al [31] proposed a competitive chemostat model with distributed delay to describe the process of nutrient consumption They proved that there existed only one survivor under any conditions and pointed out that the theoretical results in their paper were valid for all systems with monotone growth response functions. Liu et al [32] established a stochastic competitive model and obtained sufficient conditions of extinction and persistence (including weak persistence and strong persistence) They stated that only one species survived under certain stochastic noise perturbation. In this paper, considering the dilution rate of microorganisms related to the feedback control and the influence of stochastic factors from the environment, we establish the following stochastic turbidostat system based on Zhang et al [21] who constructed a stochastic chemostat model and obtained the conditions of competitive exclusion.

Existence and Uniqueness of the Positive Solution

The Principle of Competitive Exclusion

Discussion and Numerical