Extensive and Subextensive Chaos in Globally Coupled Dynamical Systems

Kazumasa A. Takeuchi, Hugues Chaté, Francesco Ginelli, Antonio Politi, and Alessandro Torcini

Phys. Rev. Lett. 107, 124101 – Published 13 September 2011

Abstract

Using a combination of analytical and numerical techniques, we show that chaos in globally coupled identical dynamical systems, whether dissipative or Hamiltonian, is both extensive and subextensive: their spectrum of Lyapunov exponents is asymptotically flat (thus extensive) at the value $λ_{0}$ given by a single unit forced by the mean field, but sandwiched between subextensive bands containing typically $O (\log N)$ exponents whose values vary as $λ ≃ λ_{\infty} + c / \log N$ with $λ_{\infty} \neq λ_{0}$ .

Received 23 March 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.124101

Authors & Affiliations

Kazumasa A. Takeuchi^1,2, Hugues Chaté¹, Francesco Ginelli^3,4,5,1, Antonio Politi^6,5, and Alessandro Torcini^6,4

¹Service de Physique de l’État Condensé, CEA–Saclay, F-91191 Gif-sur-Yvette, France
²Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
³CNR, Istituto dei Sistemi Complessi (ISC), Via dei Taurini 19, I-00185 Roma, Italy
⁴Dipartimento di Fisica and INFN, Universitá di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, Italy
⁵Department of Physics and SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
⁶CNR, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy

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Vol. 107, Iss. 12 — 16 September 2011

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