Eur. Phys. J. B (2017) 90: 7
https://doi.org/10.1140/epjb/e2016-70641-1

Regular Article

Critical fluctuations of noisy period-doubling maps

¹ Department of Environmental Science and Policy, University of California, Davis, 95616 CA, USA
² Department of Physics, University of Massachusetts, Amherst, 01003 Massachusetts, USA
³ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, 87501 NM, USA

^a e-mail: andrewenoble@gmail.com

Received: 29 August 2016
Received in final form: 14 November 2016
Published online: 16 January 2017

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.