Chaotic radial basis function network with application to dynamic modeling of chaotic time series

This paper introduces a novel algorithm for adjusting the structure of a Radial Basis Function Network (RBFN). It has been shown that Radial Basis Function Networks (RBFN's) are capable of universal approximation. This suggests the possibility of using these neural models to identify the chaotic systems. However, when we deal with the observable from some process (e.g., biological systems) whose mathematical formulation and the total number of variables may not be known exactly, structure construction and adjustment of the artificial neural network remain as an open question. In this work we introduce the chaotic dynamics in the structure construction of the RBFN. It can be seen that the radial basis functions establish a partition of the embedding space into regions in each of which it is possible to approximate the dynamics with a basis function. On account of the fact that the attractor of the chaotic systems is a fractal object, we use the fractal scaling process for partitioning the strange attractor into self-similar structures. Accordingly, the number of input variables, the number of basis function, and the scaling parameter of the basis function can be specified by the fractal scaling process. This work represents a promising approach to the modeling and prediction of chaotic time series.