Part 6: AlgorithmsInternational audienceMutual Information method is a widely used method for estimation of time delay value in the process of time delay embedding. It’s designed for a univariate scalar time series. In the real systems often many outputs of investigated system are available. In this case a multivariate time delay estimation method is necessary if one may require to perform the uniform time delay embedding. The special case of multivariate data is a kinematic time series(e.g. quaternion time series or Euler angles time series). The main goal of this paper is to provide a method for this case: Mutual Information method’s extension for quaternion time series. The results are also compared with previosly presented quaternion’s angle method. The method was tested on the real kinematic data - the recordings of human gait

Many real phenomenona preserves the properties of chaotic dynamics. However, unambiguous determination of belonging to a group of chaotic systems is difficult and complex problem. The main purpose of this paper is to present compound method of time series classification which is basically directed to the detection of chaotic behaviors. The method has been designed for differentiation of three types of time series: chaotic, periodic and random. Our approach assumes, that more reliable information about the dynamics of the system will provide the compilation of several methods, than any individual. This paper focuses on choosing a good set of methods and analysis of their results. In our investigation, we used the following methods and indicators: time delay embedding, mutual information, saturation of system invariants, the largest Lyapunov exponent and Hurst exponent. We checked the validity of the methods applying them to three kinds of basic systems which generate chaotic, periodic and random time series. As a summary of this paper, all selected methods and indicators computed for generated times series have been summarized in the table, which gives the authors a possibility to conclude about type of observed behavior.

No abstract

The series "Studies in Systems, Decision and Control" (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control-quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-

No abstract