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Adaptive identification of time delays in nonlinear dynamical models
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Ma, Huanfei, Xu, Bing, Lin, Wei and Feng, Jianfeng (2010) Adaptive identification of time delays in nonlinear dynamical models. Physical Review E, Volume 82 (Number 6). article no. 066210 . doi:10.1103/PhysRevE.82.066210 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.82.066210
Abstract
This paper develops an adaptive synchronization strategy to identify both discrete and distributed time delays in nonlinear dynamical models. In contrast with adaptive techniques for parameter estimation in the literature, the adaptive strategy developed here for time-delay identification invites more precise results that have physical and dynamical importance. It is analytically and numerically found that distributed time delays in a model with an asymptotically stable steady state can be adaptively identified, and which is different from the case of discrete time-delays identification. Other aspects of the strategy developed here, for time-delay identification, are illustrated by several representative dynamical models. Aside from illustrations for toy models and their generated data, the strategy developed is used with experimental data, to identify a time delay, called transcriptional delay, in a model describing the transcription of messenger RNAs (mRNAs) for Notch signaling molecules.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Linear models (Statistics), Dynamics, Messenger RNA -- Mathematical models | ||||
| Journal or Publication Title: | Physical Review E | ||||
| Publisher: | American Physical Society | ||||
| ISSN: | 1539-3755 | ||||
| Official Date: | 2010 | ||||
| Dates: |
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| Volume: | Volume 82 | ||||
| Number: | Number 6 | ||||
| Page Range: | article no. 066210 | ||||
| DOI: | 10.1103/PhysRevE.82.066210 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Funder: | Fu dan da xue (Shanghai, China) [Fudan University], Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC), China. Guo jia ke xue ji shu bu [Ministry of Science and Technology] (CMST), Engineering and Physical Sciences Research Council (EPSRC), European Union (EU) | ||||
| Grant number: | 60874121, 10971035, J0730103 (NNSF) ; 2007CB814904 (CMST) |
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