Analogy between the Lorenz strange attractor and a bistable stochastic oscillator

Abstract

The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing z(t) in the Lorenz model by a stochastic variableζ(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar.