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 non-trivial scaling behavior, D(L) ~ L^{-γ}, with the system size L. Here, we show that the wandering exponent γcan 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, γcan 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.

8 pages

References in corpus (6)

• Characterizing dynamics with covariant Lyapunov vectors
• Hyperbolicity and the effective dimension of spatially-extended dissipative systems
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos
• Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices
• Lyapunov analysis captures the collective dynamics of large chaotic systems
• Characteristic Lyapunov vectors in chaotic time-delayed systems

Cited by in corpus (12)

• Statistical and Dynamical Properties of Covariant Lyapunov Vectors in a Coupled Atmosphere-Ocean Model - Multiscale Effects, Geometric Degeneracy, and Error Dynamics
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Critical fluctuations and slowing down of chaos
• Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
• Faceted patterns and anomalous surface roughening driven by long-term correlated noise
• Diverging fluctuations of the Lyapunov exponents
• Self-averaging fluctuations in the chaoticity of simple fluids
• Heterogeneity of the Attractor of the Lorenz '96 Model: Lyapunov Analysis, Unstable Periodic Orbits, and Shadowing Properties
• Universal dynamic scaling in chemical reactions at and away from equilibrium
• Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
• Nonuniversal large-size asymptotics of the Lyapunov exponent in turbulent globally coupled maps
• Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos