Extensive and subextensive chaos in globally coupled dynamical systems.
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(logN) exponents whose values vary as λ≃λ(∞)+c/logN with λ(∞)≠λ(0).
Service de Physique de l'État Condensé, CEA-Saclay, F-91191 Gif-sur-Yvette, France.
Kazumasa A
KA
Takeuchi
Hugues
H
Chaté
Francesco
F
Ginelli
Antonio
A
Politi
Alessandro
A
Torcini