Geodesic
Time-series rate of convergence to quasi-periodic oscillations
Nanosistemy: fizika, himiâ, matematika, Tome 5 (2014) no. 3, pp. 354-362

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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.
Keywords: time-series, self-oscillatory modes, Lyapunov exponents
Mots-clés : convergence rate. 
@article{NANO_2014_5_3_a2,
     author = {A. V. Bespalov and E. V. Vilkova},
     title = {Time-series rate of convergence to quasi-periodic oscillations},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {354--362},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2014_5_3_a2/}
}
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A. V. Bespalov; E. V. Vilkova. Time-series rate of convergence to quasi-periodic oscillations. Nanosistemy: fizika, himiâ, matematika, Tome 5 (2014) no. 3, pp. 354-362. http://geodesic.mathdoc.fr/item/NANO_2014_5_3_a2/