The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called diffusion entropy analysis (DEA). We adopt artificial Gauss and Lévy time series, as prototypes of ordinary and anomalous statistics, respectively, and we analyze them with the DEA and four ordinary methods of analysis, some of which are very popular. We show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of Lévy statistics.

We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.

Time series of human gait stride intervals exhibit fractal and multifractal properties under several conditions. Records from subjects walking at normal, slow, and fast pace speed are analyzed to determine changes in the fractal scalings as a function of the stress condition of the system. Records from subjects with different age from children to elderly and patients suffering from neurodegenerative disease are analyzed to determine changes in the fractal scalings as a function of the physical maturation or degeneration of the system. A supercentral pattern generator model is presented to simulate the above two properties that are typically found in dynamical network performance: that is, how a dynamical network responds to stress and to evolution.