najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1020Research ArticlePHYSICSФИЗИКАTime-series rate of convergence to quasi-periodic oscillationsBespalovA. V.

Saint Petersburg

magisterbes@gmail.comVilkovaE. V.

Saint Petersburg

ITMO UniversityRussian Federation20141508202553354362Copyright © Bespalov A.V., Vilkova E.V., 20252025Bespalov A.V., Vilkova E.V.Bespalov A.V., Vilkova E.V.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1020

We propose three algorithms that can fairly accurately estimate the degree of convergence to the limit cycle using time-series generated by systems that converge to a quasi-periodic oscillation and consider their applicability ranges. As a proof-of-concept, a trivial two-dimensional case is studied. A practically important three-dimensional case is considered. Generalization of the algorithm to the space of any number of dimensions is presented. An example of these algorithms was used for estimating the Van-der-Pol system convergence.

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The authors declare that there are no conflicts of interest present.