Generalized Statistical Complexity Measure: A New Tool for Dynamical System

O. A. ROSSO; H. A. LARRONDO; M. T. MARTIN; A. PLASTINO

Pamplona, Spain

Workshop; Workshop Net-Works 2008; 2008

Universidad de Navarra, Pamplona, Spain

The generalized Statistical Complexity Measure (SCM) is a functional that characterizes the probability distribution P associated to the time series generated by a dynamical system under study. It quantifies not only randomness but also the presence of correlational structures. In this seminar several fundamental issues are reviewed: a) selection of the information measure I; b) selection of the probability metric space and its corresponding distance D; c) definition of the generalized disequilibrium Q; d) selection of the probability distribution P associated to a dynamical system or time series under study, which in fact, is a basic problem. Here we show that improvements can be expected if the underlying probability distribution is “extracted” by appropriate consideration regarding causal effects in the system’s dynamics. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed. The main achievement of this approach is the possibility of clearly distinguish between them in the Entropy-Complexity representation space, something that is rather difficult otherwise. .