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Critical fluctuations of noisy period-doubling maps

Author

Listed:
  • Andrew E. Noble

    (University of California
    University of Massachusetts)

  • Saba Karimeddiny

    (University of Massachusetts)

  • Alan Hastings

    (University of California)

  • Jonathan Machta

    (University of California
    Santa Fe Institute)

Abstract

We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These far-from-equilibrium fluctuations are described by finite-size mean field theory, placing their static properties in the same universality class as the Ising model on a complete graph. We demonstrate that the effective system size of noisy period-doubling bifurcations exhibits universal scaling behavior along period-doubling routes to chaos.

Suggested Citation

  • Andrew E. Noble & Saba Karimeddiny & Alan Hastings & Jonathan Machta, 2017. "Critical fluctuations of noisy period-doubling maps," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(1), pages 1-6, January.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:1:d:10.1140_epjb_e2016-70641-1
    DOI: 10.1140/epjb/e2016-70641-1
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    Statistical and Nonlinear Physics;

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