Chaotic Time Series Prediction Model for Fractional-Order Duffing's Oscillator

Abstract

This paper focuses on developing a prediction model for chaotic behavior in fractional-order Duffing's oscillator using neural networks. The model predicts the change in state variables' values of the oscillator using its past observations obtained by numerically solving the governing equations using the famous Grünwald-Letnikov's approach. Further, a comparison of hold-out and k-fold techniques is made using the Levenberg-Marquardt training algorithm. The results show the best-proposed model's prediction performance with mean square errors (MSE) and R2 values close to zero and one, respectively. In all the cases, the k-fold cross-validation has performed better than hold-out. However, the k-fold method has taken more computational time for training the model as it is trained k-times compared to one time using the hold-out method.