Positive Quadratic System Modeling Based on Singular Perturbation
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- OKAMOTO Yuji
- Graduate School of Information Science and Engineering, Tokyo Institute of Technology
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- IMURA Jun-ichi
- Graduate School of Engineering, Tokyo Institute of Technology
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- OKADA-HATAKEYAMA Mariko
- Institute for Protein Research, Osaka University
Bibliographic Information
- Other Title
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- 特異摂動によるポジティブ2次システムモデリング
- トクイセツドウ ニ ヨル ポジティブ 2ジ システム モデリング
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Abstract
Our previous study proposed a positive quadratic system representation for molecular interaction in a cell, including a signal transduction pathway and a gene regulatory network, and also presented a method for estimating a positive invariant set depending on the initial state. As an extension towards wider applications of this approach, this paper proposes a system representation called here a singularly perturbed positive quadratic system, and shows that every positive rational system, which is used as a mathematical model expressing biological behavior, can be approximately represented by a quasi-steady state system of a singularly perturbed positive quadratic system. In addition, we prove that the singularly perturbed positive quadratic system preserves stability at an equilibrium point of the positive rational system.
Journal
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- Transactions of the Society of Instrument and Control Engineers
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Transactions of the Society of Instrument and Control Engineers 53 (3), 251-259, 2017
The Society of Instrument and Control Engineers
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Keywords
Details 詳細情報について
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- CRID
- 1390001204510770816
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- NII Article ID
- 130005450293
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- NII Book ID
- AN00072392
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- ISSN
- 18838189
- 04534654
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- NDL BIB ID
- 028072278
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed