Time-series rate of convergence to quasi-periodic oscillations

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.