Time Series Forecasting Model for Chaotic Fractional-Order Rössler System

Abstract

Abstract This paper concentrates on developing a forecasting model to reconstruct states in a chaotic fractional-order Rössler system. The proposed model’s attractiveness is how relationships between inputs (state variables) and outputs (change in state variables) are modeled for accurate prediction. The prediction model results show the excellent tracking ability for all the changes in state variables with \({R}^2\) and MSE values close to one and zero, respectively. Also, the proposed forecasting model’s performance shows the best performance on reconstructing the states with minimal MSE errors. This best performance is valid for all three reconstructed state variables of the system.KeywordsAdams–Bashforth methodChaosForecastingFractional-order systemsNeural networks