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
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2017
