Local sensitivity of spatiotemporal structures

TL;DR

This paper introduces a local sensitivity index for spatiotemporal structures in coupled oscillators, revealing how deviations indicate noise sensitivity and the emergence of spatial chaos in complex patterns.

Contribution

It proposes a novel local sensitivity index based on finite-time Lyapunov Exponents for analyzing spatiotemporal dynamics.

Findings

Deviations of the index reflect noise sensitivity.

Index indicates onset of spatial chaos.

Applicable to nonlocally-coupled Rössler oscillators.

Abstract

We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the asymptotic scaling of local-in-space, finite-time Lyapunov Exponents. For a system of nonlocally-coupled R\"{o}ssler oscillators, we show that deviations of this index reflect the sensitivity to noise and the onset of spatial chaos for the patterns where coherence and incoherence regions coexist.