Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture
A hybrid system with state-based switchings is proposed to describe the fed-batch production of 1,3-propandiol from glycerol in our previous work. However, the on-off switching of alkali is too frequent, which greatly increases the computational cost of the numerical solution to the system so as to...
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Online Access: | http://dx.doi.org/10.1155/2012/295627 |
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doaj-8cc2ecc894364b86b91f19df62f87bbc2020-11-24T23:07:06ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/295627295627Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch CultureLei Wang0School of Mathematical Science, Dalian University of Technology, Liaoning, Dalian 116012, ChinaA hybrid system with state-based switchings is proposed to describe the fed-batch production of 1,3-propandiol from glycerol in our previous work. However, the on-off switching of alkali is too frequent, which greatly increases the computational cost of the numerical solution to the system so as to locate the state-based switchings in strict time order and implement the correct mode changes. To deal with this problem, we consider the switching of alkali pump as an impulsive event and present a nonlinear impulsive switching system to describe the fed-batch culture. It is proved that the impulsive switching system is non-Zeno. Some basic properties of solutions to the impulsive switching system are also explored. In order to overcome the discontinuities of the system, the Skorohod topology is induced and a specific form of λ is constructed to prove the main theorem. Additionally, a numerical simulation is carried out to show that the proposed system can describe the fed-batch culture properly and the essential difference with the previous work.http://dx.doi.org/10.1155/2012/295627 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lei Wang |
spellingShingle |
Lei Wang Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture Abstract and Applied Analysis |
author_facet |
Lei Wang |
author_sort |
Lei Wang |
title |
Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture |
title_short |
Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture |
title_full |
Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture |
title_fullStr |
Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture |
title_full_unstemmed |
Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture |
title_sort |
modelling and regularity of nonlinear impulsive switching dynamical system in fed-batch culture |
publisher |
Hindawi Limited |
series |
Abstract and Applied Analysis |
issn |
1085-3375 1687-0409 |
publishDate |
2012-01-01 |
description |
A hybrid system with state-based switchings is proposed to describe the fed-batch production of 1,3-propandiol from glycerol in our previous work. However, the on-off switching of alkali is too frequent, which greatly increases the computational cost of the numerical solution to the system so as to locate the state-based switchings in strict time order and implement the correct mode changes. To deal with this problem, we consider the switching of alkali pump as an impulsive event and present a nonlinear impulsive switching system to describe the fed-batch culture. It is proved that the impulsive switching system is non-Zeno. Some basic properties of solutions to the impulsive switching system are also explored. In order to overcome the discontinuities of the system, the Skorohod topology is induced and a specific form of λ is constructed to prove the main theorem. Additionally, a numerical simulation is carried out to show that the proposed system can describe the fed-batch culture properly and the essential difference with the previous work. |
url |
http://dx.doi.org/10.1155/2012/295627 |
work_keys_str_mv |
AT leiwang modellingandregularityofnonlinearimpulsiveswitchingdynamicalsysteminfedbatchculture |
_version_ |
1725620081002545152 |