Predicting Chaos

The main advantage of detecting chaos is that the time series is short term predictable. The prediction accuracy decreases in time. A strong evidence of chaotic dynamics is the existence of a positive Lyapunov exponent (i.e. sensitivity to initial conditions). In chaotic time series prediction theory the methods used can be placed in two classes: global and local methods. Neural networks are global methods of prediction. The paper tries to find a relation between the two parameters used in reconstruction of the state space (embedding dimension m and delay time τ) and the number of input neurons of a multilayer perceptron (MLP). For two of three time series studied, the minimum absolute error value is minimum for a MLP with the number of inputs equal to m*τ.