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arXiv · 1103.4536

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

Kazumasa A. Takeuchi·Hugues Chaté·Francesco Ginelli·Antonio Politi·Alessandro Torcini
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Abstract

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 $λ_0$ 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 $λ\simeq λ_\infty + c/\log N$ with $λ_\infty \neq λ_0$.

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Kazumasa A. Takeuchi, Hugues Chaté, Francesco Ginelli, Antonio Politi, Alessandro Torcini. 2011-05-16. Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems. https://doi.org/10.1103/physrevlett.107.124101

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