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Universal scaling of Lyapunov-exponent fluctuations in space-time chaos

Abstract: Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase space. A recent numerical study of spatially extended systems has revealed that the diffusion coefficient D of the Lyapunov exponents (LEs) exhibits a nontrivial scaling behavior, D(L)?L??, with the system size L. Here, we show that the wandering exponent ? can be expressed in terms of the roughening exponents associated with the corresponding ?Lyapunov surface.? Our theoretical predictions are supported by the numerical analysis of several spatially extended systems. In particular, we find that the wandering exponent of the first LE is universal: in view of the known relationship with the Kardar-Parisi-Zhang equation, ? can be expressed in terms of known critical exponents. Furthermore, our simulations reveal that the bulk of the spectrum exhibits a clearly different behavior and suggest that it belongs to a possibly unique universality class, which has, however, yet to be identified.

 Autoría: Pazó D., López J.M., Politi A.,

 Fuente: Physical Review E, 2013, 87, 062909

 Editorial: American Physical Society

 Año de publicación: 2013

 Nº de páginas: 7

 Tipo de publicación: Artículo de Revista

 DOI: 10.1103/PhysRevE.87.062909

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

 Proyecto español: FIS2009-12964-C05-05

 Url de la publicación: https://doi.org/10.1103/PhysRevE.87.062909