Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy

Li, W; Ji, J; Huang, L; Zhang, Y

Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy

Li, W Ji, J

Huang, L Zhang, Y

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Publisher:: PERGAMON-ELSEVIER SCIENCE LTD
Publication Type:: Journal Article
Citation:: Chaos, Solitons and Fractals, 2023, 167
Issue Date:: 2023-02-01

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Field	Value	Language
dc.contributor.author	Li, W
dc.contributor.author	Ji, J https://orcid.org/0000-0003-3280-5463
dc.contributor.author	Huang, L
dc.contributor.author	Zhang, Y
dc.date.accessioned	2023-11-07T01:55:13Z
dc.date.available	2023-11-07T01:55:13Z
dc.date.issued	2023-02-01
dc.identifier.citation	Chaos, Solitons and Fractals, 2023, 167
dc.identifier.issn	0960-0779
dc.identifier.issn	1873-2887
dc.identifier.uri	http://hdl.handle.net/10453/173128
dc.description.abstract	In this paper, we study the periodic solution and global stability of a chemostat model under impulsive control. First, we investigate the positivity and boundedness of the solution of the controlled system. Second, we find the periodic solution of the controlled system by employing the Poincare map and Brouwer's fixed-point theorem. Furthermore, we obtain a sufficient condition which allows the existence of orbitally stable order-k periodic solutions (k=1,2) by using the comparison method and the vector field analysis. We find that the controlled system exists a unique positive equilibrium point that is globally asymptotically stable (GAS) under some conditions. Finally, we provide two numerical examples to verify the correctness of the theoretical results.
dc.language	English
dc.publisher	PERGAMON-ELSEVIER SCIENCE LTD
dc.relation.ispartof	Chaos, Solitons and Fractals
dc.relation.isbasedon	10.1016/j.chaos.2022.113077
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	01 Mathematical Sciences, 08 Information and Computing Sciences, 09 Engineering
dc.subject.classification	Mathematical Physics
dc.subject.classification	40 Engineering
dc.subject.classification	46 Information and computing sciences
dc.subject.classification	49 Mathematical sciences
dc.title	Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy
dc.type	Journal Article
utslib.citation.volume	167
utslib.for	01 Mathematical Sciences
utslib.for	08 Information and Computing Sciences
utslib.for	09 Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access	*
dc.date.updated	2023-11-07T01:55:12Z
pubs.publication-status	Published
pubs.volume	167

Abstract:

In this paper, we study the periodic solution and global stability of a chemostat model under impulsive control. First, we investigate the positivity and boundedness of the solution of the controlled system. Second, we find the periodic solution of the controlled system by employing the Poincare map and Brouwer's fixed-point theorem. Furthermore, we obtain a sufficient condition which allows the existence of orbitally stable order-k periodic solutions (k=1,2) by using the comparison method and the vector field analysis. We find that the controlled system exists a unique positive equilibrium point that is globally asymptotically stable (GAS) under some conditions. Finally, we provide two numerical examples to verify the correctness of the theoretical results.

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http://hdl.handle.net/10453/173128