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

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 ${\lambda }_0$ 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 ${\lambda }_{\infty }\ne {\lambda }_0$.

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

References in corpus (2)

• Collective chaos in pulse-coupled neural networks
• Lyapunov analysis captures the collective dynamics of large chaotic systems

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