SPECTRAL AND CORRELATION ANALYSIS OF SPIRAL CHAOS

Abstract

We study numerically the behavior of the autocorrelation function (ACF) and the power spectrum of spiral attractors without and in the presence of noise. It is shown that the ACF decays exponentially and has two different time scales. The rate of the ACF decrease is defined by the amplitude fluctuations on small time intervals, i.e., when τ < τ cor , and by the effective diffusion coefficient of the instantantaneous phase on large time intervals. It is also demonstrated that the ACF in the Poincare map also decreases according to the exponential law exp (- λ+ k), where λ+ is the positive Lyapunov exponent. The obtained results are compared with the theory of fluctuations for the Van der Pol oscillator.