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Critical fluctuations of noisy period-doubling maps

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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.

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Authors and Affiliations

  1. Department of Environmental Science and Policy, University of California, Davis, 95616, CA, USA

    Andrew E. Noble, Alan Hastings & Jonathan Machta

  2. Department of Physics, University of Massachusetts, Amherst, 01003, Massachusetts, USA

    Andrew E. Noble & Saba Karimeddiny

  3. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, 87501, NM, USA

    Jonathan Machta

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  1. Andrew E. Noble
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  2. Saba Karimeddiny
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  3. Alan Hastings
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Correspondence to Andrew E. Noble.

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Noble, A.E., Karimeddiny, S., Hastings, A. et al. Critical fluctuations of noisy period-doubling maps. Eur. Phys. J. B 90, 7 (2017). https://doi.org/10.1140/epjb/e2016-70641-1

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