Spectral Structure and Universality of Intermittent Chaos

Abstract

A time series of intermittent chaos is changed by bursts suddenly, and its amplitude and phase jump randomly. Between the bursts, the time series oscillates with slow amplitude modulations. Thus the time series is a random sequence of periodic states with different lifetimes, amplitude modulations and phase shifts. Such time series are observed in various systems extending from the pendulum driven by a periodic force to the Bénard convection of fluids. This universality is quantitatively represented by an inverse-power law of the envelope of equally-spaced Lorentzian lines in the power spectrum of the time series near the onset point. The exponents of the separation and widths of the Lorentzian lines are determined within a mean-field framework.