The Effect of Noise in Time Series Analysis


Mengyang Sun

Deterministic chaos was observed by Zhang et al. in a simple network of electronic logic gates that are not regulated by a clocking signal. They use the Boolean distance between segments of two nearby trajectories to characterize the chaotic fluctuations of the voltage measured at a given point in the circuit[1]. We use a more general method to test their analysis. We use time delay coordinates to obtain a trajectory in an embedding phase space. When we look at the divergence of two portions of the trajectory that begin at nearby points, some unusual phenomena can be observed that are thought to be due to noise. We analyze the effects of two types of noise on some well-studied chaotic and non-chaotic systems to better understand the source of these phenomena and the features of the electrical time series.

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