Statistical Classification Of Chaotic Signals

The classification of chaotic signals generated by a low-dimensional deterministic models given a dictionary of possible model is considered. The proposed classification methods rely on the concept of "best predictor" of signal. A statistical interpretation of this concept based on the ergodic theory of chaotic system is presented. A sort of "bootstrapping" estimator of the statistical properties is introduced. The method is validated by numerical simulations. Directions for future research are suggested. 1. INTRODUCTION Also known under the popular name of "chaos theory," the theory of nonlinear dynamical system has been the subject of considerable advances over the past twenty years. Chaotic systems are deterministic dynamical systems with a small number of degrees of freedom whose behavior appears, in a sense, random and unpredictable. Most of the early research efforts on chaos theory have been the fact of mathematicians and physicists. Mathematical and computational tools for the..