Sensitivity Analysis for Oscillating Dynamical Systems
Name
Wilkins-2009-SENSITIVITY ANALYSIS.pdf
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622.51 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
White, Jacob K.
Tidor, Bruce
Wilkins, A. Katharina
Barton, Paul I.
Date Issued
June 2009
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Wilkins, A. Katharina et al. “Sensitivity Analysis for Oscillating Dynamical Systems.” SIAM Journal on Scientific Computing 31.4 (2009): 2706-2732. ©2009 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
Boundary value formulations are presented for exact and efficient sensitivity analysis, with respect to model parameters and initial conditions, of different classes of oscillating systems. Methods for the computation of sensitivities of derived quantities of oscillations such as period, amplitude, and different types of phases are first developed for limit-cycle oscillators. In particular, a novel decomposition of the state sensitivities into three parts is proposed to provide an intuitive classification of the influence of parameter changes on period, amplitude, and relative phase. The importance of the choice of time reference, i.e., the phase locking condition, is demonstrated and discussed, and its influence on the sensitivity solution is quantified. The methods are then extended to other classes of oscillatory systems in a general formulation. Numerical techniques are presented to facilitate the solution of the boundary value problem and the computation of different types of sensitivities. Numerical results are verified by demonstrating consistency with finite difference approximations and are superior both in computational efficiency and in numerical precision to existing partial methods.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1137/070707129
