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Nonuniversal large-size asymptotics of the Lyapunov exponent in turbulent globally coupled maps

Abstract: Globally coupled maps (GCMs) are prototypical examples of high-dimensional dynamical systems. Interestingly, GCMs formed by an ensemble of weakly coupled identical chaotic units generically exhibit a hyperchaotic ?turbulent? state. A decade ago, Takeuchi et al. [Phys. Rev. Lett. 107, 124101 (2011)] theorized that in turbulent GCMs the largest Lyapunov exponent (LE), ?(N), depends logarithmically on the system size N: ????(N)?c/lnN. We revisit the problem and analyze, by means of analytical and numerical techniques, turbulent GCMs with positive multipliers to show that there is a remarkable lack of universality, in conflict with the previous prediction. In fact, we find a power-law scaling ????(N)?c/N?, where ? is a parameter-dependent exponent in the range 0

 Fuente: Physical Review E. Vol. 104, 3-September 2021, 034216

Editorial: American Physical Society

 Año de publicación: 2021

Nº de páginas: 12

Tipo de publicación: Artículo de Revista

 DOI: https://doi.org/10.1103/PhysRevE.104.034216

ISSN: 1539-3755,1550-2376,2470-0045,2470-0053

Proyecto español: FIS2016-74957-P

Url de la publicación: https://doi.org/10.1103/PhysRevE.104.034216