Algorithmic Complexity Measure and Lyapanov matrices of the Dynamical Systems

The problem of distinguishing order from disorder in dynamical systems can be answered by certain quantities such as Lyapanov exponents, fractal dimensions, power spectrum density, and algorithmic complexity measures. In this paper, we have compared two approaches to evaluate the order and disorder in dynamic systems behavior. First, this is done by mapping the system output signal to a binary string and calculating the complexity measure of the time-series data. The results from algorithmic complexity are compared with the results from Lyapunov metrics computation. Using these two metrics, we can distinguish noise from chaos and order. This is important because modern engineering disciplines deal with signals acquired in the form of time series. The signals obtained from biological, electrical or mechanical systems appear to be complex. Therefore by extracting their characteristic features in such processes, one can make a correlation to a certain class of perception or behavior in cognitive sciences. This can be used for better analysis, control and diagnosis.