Optimal Phase Description of Chaotic Oscillators

TL;DR

This paper develops an optimal phase description for chaotic oscillators by generalizing isochrones, leading to a maximally decoupled phase that accurately describes phase resetting, demonstrated on Rössler and Lorenz systems.

Contribution

It introduces a novel method to define optimal isophases in chaotic systems, improving phase analysis and resetting descriptions.

Findings

Optimal isophases show nearly constant return times.

The method effectively decouples amplitude and phase dynamics.

Demonstrated on Rössler and Lorenz chaotic systems.

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.