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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/295627 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556755713785856 |
|---|---|
| author | Lei Wang |
| author_facet | Lei Wang |
| author_sort | Lei Wang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8cc2ecc894364b86b91f19df62f87bbc |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8cc2ecc894364b86b91f19df62f87bbc2025-02-03T05:44:23ZengWileyAbstract 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 |
| spellingShingle | Lei Wang Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture Abstract and Applied Analysis |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/295627 |
| work_keys_str_mv | AT leiwang modellingandregularityofnonlinearimpulsiveswitchingdynamicalsysteminfedbatchculture |