title: Adaptive identification of time delays in nonlinear dynamical models.
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.
authors.affiliation: School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai, China.
authors.forename: Huanfei
authors.initials: H
authors.lastname: Ma
authors.forename: Bing
authors.initials: B
authors.lastname: Xu
authors.forename: Wei
authors.initials: W
authors.lastname: Lin
authors.forename: Jianfeng
authors.initials: J
authors.lastname: Feng
mesh_terms: D008954:Models, Biological; D017711:Nonlinear Dynamics; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism; D051880:Receptors, Notch / Q000235:genetics / Q000378:metabolism; D013997:Time Factors; D014158:Transcription, Genetic
chemical_list: D012333:RNA, Messenger; D051880:Receptors, Notch