ABSTRACT
This chapter describes the ways of optimizing predictive chaotic model parameters leading to more accurate predictions. Three methods, grid search, genetic algorithms and adaptive cluster covering, are discussed and implemented for optimizing predictive chaotic model.
8.1 Introduction The characteristics of the strange attractors of a chaotic system can be analyzed by sampling a part of the output chaotic time series of a system. The method that is commonly used is the state space reconstruction in delay coordinate proposed by Packard et al. (1980). Further, Floris Takens introduced his famous Taken's theorem stating that the unstable periodic obits (strange attractor) could be recovered properly in an embedding space whenever a suitable embedding dimension m≥2d+1 (d is the dimension of chaotic system) is detected; that is, the orbits in the reconstructed space Rm keeps a differential homeomorphism with the original system (Takens, 1981). It is very important to select a suitable pair of embedding dimension m and time delay τ when performing the phase space reconstruction. The precision of τ and m is directly related with the accuracy of the invariables of the described characteristics of the strange attractors in phase space reconstruction. There exist two different points of view for doing this.
