Scaling Theory for Noisy Period-Doubling Transitions to Chaos

The effect of noise on systems which undergo period-doubling transitions to chaos is studied. With the aid of nonequilibrium field-theoretic techniques, a correlation-function expression for the Lyapunov parameter (which describes the sensitivity of the system to initial conditions) is derived and shown to satisfy a scaling theory. Since these transitions have previously been shown to exhibit universal behavior, this theory predicts universal effects for the noise. These predictions are in good agreement with numerical experiments.