THEORY FOR RELAXATION AT A SUBCRITICAL PITCHFORK BIFURCATION

A theory is presented for the transient process of decay from the state of marginal stability occurring in a subcritical pitchfork bifurcation. We introduce an approximation for the stochastic paths that allows the calculation of a generating function for the statistics of the escape time. The time-dependent moments and transient fluctuations are calculated from the distribution of passage times by a scaling transformation that is associated with initial non-Gaussian statistics. Our results are in agreement with numerical simulations reported also here. © 1990 The American Physical Society.