Optimal Phase Description of Chaotic Oscillators
Chaotic Dynamics
2015-05-30 v1
Abstract
We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincar\'e surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled of the amplitude dynamics, and provides a proper description of phase resetting of chaotic oscillations. The method is illustrated with the R\"ossler and Lorenz systems.
Cite
@article{arxiv.1110.4190,
title = {Optimal Phase Description of Chaotic Oscillators},
author = {Justus T. C. Schwabedal and Arkady Pikovsky and Björn Kralemann and Michael Rosenblum},
journal= {arXiv preprint arXiv:1110.4190},
year = {2015}
}
Comments
10 Pages, 14 Figures