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

Diego Pazó*, Juan M. López, Antonio Politi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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 -γ, with the system size L. Here, we show that the wandering exponent γ 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, γ 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.

Original languageEnglish
Article number062909
Pages (from-to)1-7
Number of pages7
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number6
Early online date17 Jun 2013
Publication statusPublished - Jun 2013

Bibliographical note

D.P. acknowledges support from Ministerio de Economıa y Competitividad (Spain), under a Ramon y Cajal fellowship, and from Cantabria International Campus. J.M.L. and D.P. acknowledge financial support from Ministerio de Ciencia e Innovacion (Spain) through Project No. FIS2009-12964-C05-05.


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