@article{10902/24620,
year = {2021},
url = {http://hdl.handle.net/10902/24620},
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), λ(N), depends logarithmically on the system size N: λ∞−λ(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 λ∞−λ(N)≃c/Nγ, where γ is a parameter-dependent exponent in the range 0<γ≤1. However, for strongly dissimilar multipliers, the LE varies with N in a slower fashion, which is here numerically explored. Although our analysis is only valid for GCMs with positive multipliers, it suggests that a universal convergence law for the LE cannot be taken for granted in general GCMs.},
organization = {D.V. acknowledges support by Agencia Estatal de Investigación (Spain), and European Social Fund (EU) under Grant No. BES-2017-081808 of the FPI Programme. We acknowledge support by Agencia Estatal de Investigación (Spain), and European Regional Development Fund (EU) under Project No. FIS2016-74957-P (AEI/FEDER, EU).},
publisher = {American Physical Society},
publisher = {Physical Review E. Vol. 104, 3-September 2021, 034216},
title = {Nonuniversal large-size asymptotics of the Lyapunov exponent in turbulent globally coupled maps},
author = {Velasco González, David and López Martín, Juan Manuel and Pazó Bueno, Diego Santiago},
}