Prediction of chaotic time-series with different MLE values using FPGA-based ANNs
Ana Dalia Pano-Azucena, Esteban Tlelo‐Cuautle, Luis Gerardo de la Fraga, Carlos Sánchez-López, Jose Rangel‐Magdaleno, Sheldon X.-D. Tan · 2017
Chaotic time series can be generated from different kinds of chaotic oscillators in different dimensions and directions. However, their prediction becomes a challenge when they have different values of their maximum Lyapunov exponent (MLE), which is associated to the degree of unpredictability of a chaotic system. In this manner, we highlight how an artificial neural network (ANN) can be used to predict chaotic time series with different MLE value. The cases of study are three chaotic time series with different MLE values, which are predicted by an ANN that is validated through measuring the mean square error (MSE) and root MSE (RMSE). We provide design and training details of a 5-layers ANN, and its implementation using field-programmable gate arrays. Finally, the ANN is validated with the prediction results that are compared to the original chaotic time series according to their MSE and RMSE.