Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol
In this paper, we consider a nonlinear multi-stage dynamic system to characterize batch culture. We construct corresponding linear variational system for the solution to the multi-stage system, also prove the boundedness of fundamental matrix solutions for the linear variational system. On this bas...
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Vilnius Gediminas Technical University
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doaj-669d79f35a534b1c83236a11551e1f702021-07-02T12:07:26ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102016-03-0121210.3846/13926292.2016.1142481Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-PropanediolJinxing Zhang0Jinlong Yuan1Enmin Feng2Hongchao Yin3Zhilong Xiu4School of Mathematical Sciences, Dalian University of Technology Dalian, 116024 Liaoning, China; School of Energy and Power Engineering, Dalian University of Technology Dalian, 116024 Liaoning, ChinaSchool of Mathematical Sciences, Dalian University of Technology Dalian, 116024 Liaoning, China; School of Energy and Power Engineering, Dalian University of Technology Dalian, 116024 Liaoning, China; School of Life Science and Biotechnology, Dalian University of Technology Dalian, 116024 Liaoning, ChinaSchool of Mathematical Sciences, Dalian University of Technology Dalian, 116024 Liaoning, ChinaSchool of Energy and Power Engineering, Dalian University of Technology Dalian, 116024 Liaoning, ChinaSchool of Life Science and Biotechnology, Dalian University of Technology Dalian, 116024 Liaoning, China In this paper, we consider a nonlinear multi-stage dynamic system to characterize batch culture. We construct corresponding linear variational system for the solution to the multi-stage system, also prove the boundedness of fundamental matrix solutions for the linear variational system. On this basis, we prove strong stability with respect to perturbance of initial state vector for the multi-stage system through the application of such boundedness. From extensive simulation study, it is observed that the strong stability is highly satisfactory. https://journals.vgtu.lt/index.php/MMA/article/view/801nonlinear multi-stage systemlinear variational systemfundamental matrix solutionstrong stability |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jinxing Zhang Jinlong Yuan Enmin Feng Hongchao Yin Zhilong Xiu |
spellingShingle |
Jinxing Zhang Jinlong Yuan Enmin Feng Hongchao Yin Zhilong Xiu Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol Mathematical Modelling and Analysis nonlinear multi-stage system linear variational system fundamental matrix solution strong stability |
author_facet |
Jinxing Zhang Jinlong Yuan Enmin Feng Hongchao Yin Zhilong Xiu |
author_sort |
Jinxing Zhang |
title |
Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol |
title_short |
Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol |
title_full |
Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol |
title_fullStr |
Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol |
title_full_unstemmed |
Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol |
title_sort |
strong stability of a nonlinear multi-stage dynamic system in batch culture of glycerol bioconversion to 1,3-propanediol |
publisher |
Vilnius Gediminas Technical University |
series |
Mathematical Modelling and Analysis |
issn |
1392-6292 1648-3510 |
publishDate |
2016-03-01 |
description |
In this paper, we consider a nonlinear multi-stage dynamic system to characterize batch culture. We construct corresponding linear variational system for the solution to the multi-stage system, also prove the boundedness of fundamental matrix solutions for the linear variational system. On this basis, we prove strong stability with respect to perturbance of initial state vector for the multi-stage system through the application of such boundedness. From extensive simulation study, it is observed that the strong stability is highly satisfactory.
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topic |
nonlinear multi-stage system linear variational system fundamental matrix solution strong stability |
url |
https://journals.vgtu.lt/index.php/MMA/article/view/801 |
work_keys_str_mv |
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1721330399153487872 |