Reconstruction of Chaotic Attractor for Fractional-order Tamaševičius System Using Recurrent Neural Networks

Abstract

In this paper, a forecasting model using recur-rent neural networks (RNN) for reconstructing the chaotic fractional-order Tamaševičius system states has been developed. The attractiveness of the proposed model is in the developed relationships between inputs, which are state variables, and outputs, which are the change in state variables for accurate prediction. The results from the proposed model show the best prediction ability for all three output variables with the highest R2 and the least mean square errors. The proposed forecasting model also performs best in reconstructing all three system states with minimal mean square errors.