Optimal Phase Description of Chaotic Oscillators

Details Optimal Phase Description of Chaotic Oscillators Optimal Phase Description of Chaotic Oscillators

2011-10-19

arxiv.org/abs/1110.4190v1

Nonlinear Sciences

Chaotic Dynamics

10 Pages, 14 Figures

Scientific paper

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.

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