Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators

TL;DR

This paper investigates how strange nonchaotic attractors influence the spatial dynamics of out-of-time-ordered correlators in coupled map lattices, revealing characteristic spreading patterns and dynamical regimes.

Contribution

It introduces a novel analysis of SNA effects on OTOC spread in CMLs using IS and FTLEs, supported by multiple validation tools.

Findings

OTCs exhibit on and off spreading in SNA regimes

Diverse dynamical regimes mapped in phase diagram

Presence of SNA confirmed by multiple measures

Abstract

We study the spatial spread of out-of-time-ordered correlators (OTOCs) in coupled map lattices (CMLs) of quasiperiodically forced nonlinear maps. We use instantaneous speed (IS) and finite-time Lyapunov exponents (FTLEs) to investigate the role of strange non-chaotic attractors (SNAs) on the spatial spread of the OTOC. We find that these CMLs exhibit a characteristic on and off type of spread of the OTOC for SNA. Further, we provide a broad spectrum of the various dynamical regimes in a two-parameter phase diagram using IS and FTLEs. We substantiate our results by confirming the presence of SNA using established tools and measures, namely the distribution of finite-time Lyapunov exponents, phase sensitivity, spectrum of partial Fourier sums, and $0-1$ test.