A stochastic model  for microbial fermentation process under Gaussian white noise environment

Yan  Wang; Lei  Wang; Yanxiang  Zhao; Aimin  Song; Yanping  Ma

doi:10.3934/naco.2015.5.381

Article Contents

2015, Volume 5, Issue 4: 381-392. Doi: 10.3934/naco.2015.5.381

This issue Previous Article Nonlinear state-dependent impulsive system in fed-batch culture and its optimal control Next Article Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol

A stochastic model for microbial fermentation process under Gaussian white noise environment

1.
School of Science, Dalian Jiaotong University,Dalian, MO 116028
2.
School of Mathematical Sciences, Dalian University of Technology, Dalian, MO 116023
3.
Department of Mathematics, The George Washington University,Washington DC 20052
4.
Department of Mathematics, Loyola Marymount University, Los Angeles CA 90045

Received: March 2015

Revised: October 2015

Published: October 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.

Keywords:

Mathematics Subject Classification: Primary: 60H40, 91B70, 91B74 Secondary: 60H10.

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