Mixing and spectral-correlation properties of chaotic and stochastic systems: Numerical and physical experiments

Abstract

In the present paper, we analyse a mechanism of the onset of mixing and its interconnection with exponential instability of trajectories. We study statistical characteristics of chaotic oscillations that correspond to attractors of the spiral type and of the Lorenz type. It has been established that a random process of the 'harmonic noise' type can serve as a mathematical model of spiral chaos and a random telegraph signal as a model of the Lorenz attractor. It has been revealed that the instantaneous phase dynamics plays an important role in the case of spiral chaos and determines regularities of autocorrelation decay and power spectrum formation. The effect of external Gaussian noise sources on characteristics of chaotic oscillations is analysed in detail. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.