Reconstruction of chaotic dynamics using structurally adaptive radial basis function networks

Time series prediction is based on reconstruction of unknown, possibly chaotic dynamics using a certain number of delayed values of the time series and realizing the mapping between them and future values. The number of previous values used for reconstruction (usually called the embedding dimension) strongly influences the complexity of the mapping. We have applied structurally adaptive RBF networks to determine the embedding dimension and to realize the desired mapping between the past and future values. The method is tested on reconstruction of Henon maps and Lorenz chaotic attractors.