Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol

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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Main Authors: Jinxing Zhang, Jinlong Yuan, Enmin Feng, Hongchao Yin, Zhilong Xiu
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2016-03-01
Series:Mathematical Modelling and Analysis
Subjects:
nonlinear multi-stage system
linear variational system
fundamental matrix solution
strong stability
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/801
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spelling 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.
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 AT jinxingzhang strongstabilityofanonlinearmultistagedynamicsysteminbatchcultureofglycerolbioconversionto13propanediol
AT jinlongyuan strongstabilityofanonlinearmultistagedynamicsysteminbatchcultureofglycerolbioconversionto13propanediol
AT enminfeng strongstabilityofanonlinearmultistagedynamicsysteminbatchcultureofglycerolbioconversionto13propanediol
AT hongchaoyin strongstabilityofanonlinearmultistagedynamicsysteminbatchcultureofglycerolbioconversionto13propanediol
AT zhilongxiu strongstabilityofanonlinearmultistagedynamicsysteminbatchcultureofglycerolbioconversionto13propanediol
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