NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2014, 5 (3), P. 354-362
TIME-SERIES RATE OF CONVERGENCE TO QUASI-PERIODIC OSCILLATIONS
A. V. Bespalov – ITMO University, Saint Petersburg, Russia; email@example.com
E. V. Vilkova – ITMO University, Saint Petersburg, Russia
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, convergence rate.