Critical fluctuations of noisy period-doubling maps

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.

11 pages, 5 figures

References in corpus (6)

• Environmental vs. demographic variability in two-species predator-prey models
• Anomalous mean-field behavior of the fully connected Ising model
• Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos
• Intrinsic noise and discrete-time processes
• Critical properties of phase transitions in lattices of coupled logistic maps
• The theory of individual based discrete-time processes