Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems

Details Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems

2011-03-23

arxiv.org/abs/1103.4536v2

Phys. Rev. Lett. 107, 124101 (2011)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures; minor changes made and 2 figure panels added

Scientific paper

10.1103/PhysRevLett.107.124101

Using a combination of analytical and numerical techniques, we show that chaos in globally-coupled identical dynamical systems, be they dissipative or Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov exponents is asymptotically flat (thus extensive) at the value $\lambda_0$ given by a single unit forced by the mean-field, but sandwiched between sub-extensive bands containing typically $\mathcal{O}(\log N)$ exponents whose values vary as $\lambda \simeq \lambda_\infty + c/\log N$ with $\lambda_\infty \neq \lambda_0$.

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