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

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.

12 pages, 16 figures, 2 tables

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Cited by in corpus (3)

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• Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
• Localization of information driven by stochastic resetting