TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS

0566289 - ÚTIA 2024 RIV CZ eng C - Conference Paper (international conference)
Papáček, Štěpán - Matonoha, Ctirad
TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS.
Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar. Praha: Institute of Mathematics CAS Prague, 2023 - (Chleboun, J.; Kůs, P.; Papež, J.; Rozložník, M.; Segeth, K.; Šístek, J.), s. 163-172. ISBN 978-80-85823-73-8.
[Programs and Algorithms of Numerical Mathematics 21, PANM 21 /2022/. Jablonec nad Nisou (CZ), 19.06.2022-24.06.2022]
R&D Projects: GA ČR(CZ) GA21-03689S
Institutional support: RVO:67985556 ; RVO:67985807
Keywords : Dynamical system * Singular perturbation * Averaging * Parameter estimation * Slow-fast decomposition * Damped oscillations
OECD category: Applied mathematics; Pure mathematics (UIVT-O)
http://library.utia.cas.cz/separaty/2023/TR/papacek-0566289.pdf

Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.
Permanent Link: https://hdl.handle.net/11104/0337768