Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

TL;DR

This paper introduces measures based on recurrence properties to distinguish phase-coherent from noncoherent chaos, using numerical analysis of the Rössler and Mackey-Glass systems, highlighting the effectiveness of geometric recurrence network measures.

Contribution

It proposes novel recurrence-based measures from geometric and dynamic perspectives to differentiate types of chaos, validated through numerical analysis of well-known chaotic systems.

Findings

Geometric measures effectively trace chaos transitions

Recurrence network analysis distinguishes spiral- and screw-type chaos

Attractor geometry explains observed chaotic behaviors

Abstract

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic R\"ossler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.