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Título: | Nonuniversal large-size asymptotics of the Lyapunov exponent in turbulent globally coupled maps |
Autor: | Velasco, David CSIC ORCID; López, Juan M. CSIC ORCID ; Pazó, Diego CSIC ORCID | Fecha de publicación: | 2021 | Editor: | American Physical Society | Citación: | Physical Review E 104(3): 034216 (2021) | Resumen: | 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. | Versión del editor: | https://doi.org/10.1103/PhysRevE.104.034216 | URI: | http://hdl.handle.net/10261/269400 | DOI: | 10.1103/PhysRevE.104.034216 | E-ISSN: | 2470-0053 |
Aparece en las colecciones: | (IFCA) Artículos |
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