Nonlinear methods for the determination of dynamic evolution of a time series

This paper talk addresses a new signal processing method for detecting chaos in time series. This procedure could replace other methods such as the maximal Lyapunov exponent search, and it is based on models related to the wavelet transform and chaos theory. As it will be seen, this method aims to determine a parameter, usually indicated as Kω, that allows to characterize the regularity of the dynamic evolution of the series in a very simple way. In fact this parameter tends to 1 for chaotic dynamics, otherwise it tends to 0 for regular dynamics. Moreover this sort of binary test is directly applicable to time series data (e. g. vibrational signals) even though affected by noise. In fact in this latter case is possible to reduce noise level by preliminary processing the data with a nonlinear wavelet transform called “adaptative”, modelled on the shape, frequency, amplitude and energy of the time series and consequently determine Kω based on the value of the details coefficients obtained from the convolution.