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Central limit behavior in the Kuramoto model at the “edge of chaos”

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  • Miritello, Giovanna
  • Pluchino, Alessandro
  • Rapisarda, Andrea

Abstract

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the “edge of chaos” (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like limit distributions naturally emerge, consistently with recently proved generalizations of the CLT.

Suggested Citation

  • Miritello, Giovanna & Pluchino, Alessandro & Rapisarda, Andrea, 2009. "Central limit behavior in the Kuramoto model at the “edge of chaos”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4818-4826.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:23:p:4818-4826
    DOI: 10.1016/j.physa.2009.08.023
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    Cited by:

    1. Cirto, Leonardo J.L. & Assis, Vladimir R.V. & Tsallis, Constantino, 2014. "Influence of the interaction range on the thermostatistics of a classical many-body system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 286-296.

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