Influence of Measuring System Noise on the Fractal Dimension of the Chaotic Signal Attractor

The present paper investigates the influence of stochastic noise on the estimation of the fractal dimension of the chaotic signal attractor for additive and multiplicative noises in the frequency and time domain. A simplified analogue measuring system noise model was proposed as the amplitude and phase noise in the Fourier domain, which was the equivalent of multiplicative and additive noise in the time domain. A numerical experiment was performed, which introduced noise of various intensities into the chaotic signal from the Chua system. It has been shown that in the logarithmic diagram of the correlation integral, additional scaling regions appear, the range of which increases with increasing noise intensity, causing dimension estimation errors. It has also been shown that without a thorough analysis of the correlation integral, deterministic noise can be easily confused with stochastic noise in the frequency domain.