Prediction of Duffing Chaotic time series using focused time lagged recurrent neural network model

In this paper, a focused time lagged recurrent neural network (FTLRNN) model with gamma memory is developed for multi step ahead (k=1,5,10.20,50,100) prediction of typical Duffing Chaotic time series. It is popularized in Neural network field due to its richness in chaotic behavior. It is observed that duffing time series exhibit a rich chaotic behavior. This paper compares the performance of two neural network configurations namely a Multilayer Perceptron (MLP) and proposed FTLRNN with gamma memory. The standard back propagation algorithm with momentum term has been used for both the models. It is seen that estimated dynamic FTLRNN based model with gamma memory filter clearly outperforms the MLP NN in various performance matrices such as Mean square error (MSE), Normalized mean square error (NMSE) and correlation coefficient ( r) on testing as well as training data set for Multi step prediction (K= 1,5,10,20,50,100). In addition, the output of proposed neural network model closely follows the desired output for multi step ahead prediction. It is shown that suggested FTLRNN model has the remarkable capability of time series prediction. The major contribution of this paper is that Various parameters like number of processing elements, step size, momentum value in hidden layer, in output layer the various transfer functions like tanh, sigmoid, linear-tan-h and linear sigmoid, different error norms L1,L2 ,Lp to L infinity, and different combination of training and testing samples are exhaustively experimented for obtaining the proposed robust model for long term (k=20,50,100) step as well as short step ahead (k=1,5,10)prediction.