Hopf Bifurcation Dynamics in a Delayed Turbidostat Model with Adaptive Proportional–Integral Control: Resource-Species Feedback and Stability Transitions.
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| Title: | Hopf Bifurcation Dynamics in a Delayed Turbidostat Model with Adaptive Proportional–Integral Control: Resource-Species Feedback and Stability Transitions. |
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| Authors: | Zhao, Binyu1 (AUTHOR), Mu, Yu1 (AUTHOR) muxiaoyuer12@163.com, Tan, Yuanshun1 (AUTHOR), Liu, Zijian1 (AUTHOR) |
| Source: | International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Jan2026, Vol. 36 Issue 1, p1-23. 23p. |
| Subjects: | Hopf bifurcations, Bifurcation theory, Bioreactors, Oscillations, Mathematical models, Adaptive control systems, Microbial cultures, Ecosystem dynamics |
| Abstract: | In ecosystems, the interplay between resource dynamics and species evolution drives complex adaptive behaviors of species. This study proposes a novel delayed turbidostat model that integrates resource consumption-induced delay and dynamic feedback between species and resources, aiming to elucidate oscillation patterns observed in microbial cultivation. We first establish the existence and stability criteria for the positive equilibrium, identifying conditions for steady-state coexistence without delay. Bifurcation and sensitivity analysis for the control parameters reveals that it governs Hopf bifurcation-induced periodic solutions, aligning with experimental observations of population oscillations. Furthermore, the delay parameter is shown to destabilize the equilibrium through Hopf bifurcation, while adaptive control strategies effectively increase the critical delay threshold for bifurcation, mitigating its destabilizing effects. Numerical simulations validate the theoretical framework and uncover various stability regimes under the coupled effects of delay and control scheme. Our findings provide a mechanistic understanding of how feedback control can counteract time-delay disturbances, offering practical insights for optimizing bioreactor operations and ecological management. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 190667805 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Hopf Bifurcation Dynamics in a Delayed Turbidostat Model with Adaptive Proportional–Integral Control: Resource-Species Feedback and Stability Transitions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhao%2C+Binyu%22">Zhao, Binyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mu%2C+Yu%22">Mu, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> muxiaoyuer12@163.com</i><br /><searchLink fieldCode="AR" term="%22Tan%2C+Yuanshun%22">Tan, Yuanshun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Zijian%22">Liu, Zijian</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Jan2026, Vol. 36 Issue 1, p1-23. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Hopf+bifurcations%22">Hopf bifurcations</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Bioreactors%22">Bioreactors</searchLink><br /><searchLink fieldCode="DE" term="%22Oscillations%22">Oscillations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Adaptive+control+systems%22">Adaptive control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Microbial+cultures%22">Microbial cultures</searchLink><br /><searchLink fieldCode="DE" term="%22Ecosystem+dynamics%22">Ecosystem dynamics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In ecosystems, the interplay between resource dynamics and species evolution drives complex adaptive behaviors of species. This study proposes a novel delayed turbidostat model that integrates resource consumption-induced delay and dynamic feedback between species and resources, aiming to elucidate oscillation patterns observed in microbial cultivation. We first establish the existence and stability criteria for the positive equilibrium, identifying conditions for steady-state coexistence without delay. Bifurcation and sensitivity analysis for the control parameters reveals that it governs Hopf bifurcation-induced periodic solutions, aligning with experimental observations of population oscillations. Furthermore, the delay parameter is shown to destabilize the equilibrium through Hopf bifurcation, while adaptive control strategies effectively increase the critical delay threshold for bifurcation, mitigating its destabilizing effects. Numerical simulations validate the theoretical framework and uncover various stability regimes under the coupled effects of delay and control scheme. Our findings provide a mechanistic understanding of how feedback control can counteract time-delay disturbances, offering practical insights for optimizing bioreactor operations and ecological management. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0218127426500100 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 1 Subjects: – SubjectFull: Hopf bifurcations Type: general – SubjectFull: Bifurcation theory Type: general – SubjectFull: Bioreactors Type: general – SubjectFull: Oscillations Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Adaptive control systems Type: general – SubjectFull: Microbial cultures Type: general – SubjectFull: Ecosystem dynamics Type: general Titles: – TitleFull: Hopf Bifurcation Dynamics in a Delayed Turbidostat Model with Adaptive Proportional–Integral Control: Resource-Species Feedback and Stability Transitions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhao, Binyu – PersonEntity: Name: NameFull: Mu, Yu – PersonEntity: Name: NameFull: Tan, Yuanshun – PersonEntity: Name: NameFull: Liu, Zijian IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02181274 Numbering: – Type: volume Value: 36 – Type: issue Value: 1 Titles: – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering Type: main |
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