Lyapunov analysis captures the collective dynamics of large chaotic systems

Abstract

We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting collectively on the trajectory. For globally-coupled maps, we show moreover a quantitative correspondence between the collective modes and some of the so-called Perron-Frobenius dynamics. Our results imply that the conventional definition of extensivity must be changed as soon as collective dynamics sets in.

4 pages, 4 figures; small changes, mostly stylistic, made in v2

References in corpus (1)

• Characterizing dynamics with covariant Lyapunov vectors

Cited by in corpus (10)

• Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State
• Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equation
• Collective dynamics in sparse networks
• Topological synchronization of coupled nonlinear oscillators
• Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices
• Quasi phase reduction of all-to-all strongly coupled $\lambda -\omega$ oscillators near incoherent states
• Backward and covariant Lyapunov vectors and exponents for hard disk systems with a steady heat current
• Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps
• Local integrability breaking and exponential localization of leading Lyapunov vectors
• Covariant Lyapunov vectors as global solutions of a partial differential equation on the phase space