<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper proposes novel forecasting models for fractional-order chaotic oscillators, such as Duffing’s, Van der Pol’s, Tamaševičius’s and Chua’s, using feedforward neural networks. The models predict a change in the state values which bears a weighted relationship with the oscillator states. Such an arrangement is a suitable candidate model for out-of-sample forecasting of system states. The proposed neural network-assisted weighted model is applied to the above oscillators. The improved out-of-sample forecasting results of the proposed modeling strategy compared with the literature are comprehensively analyzed. The proposed models corresponding to the optimal weights result in the least mean square error (MSE) for all the system states. Further, the MSE for the proposed model is less in most of the oscillators compared with the one reported in the literature. The proposed prediction model’s out-of-sample forecasting plots show the best tracking ability to approximate future state values.</p>
</abstract>

This paper proposes novel forecasting models for fractional-order chaotic oscillators, such as Duffing’s, Van der Pol’s, Tamaševičius’s and Chua’s, using feedforward neural networks. The models predict a change in the state values which bears a weighted relationship with the oscillator states. Such an arrangement is a suitable candidate model for out-of-sample forecasting of system states. The proposed neural network-assisted weighted model is applied to the above oscillators. The improved out-of-sample forecasting results of the proposed modeling strategy compared with the literature are comprehensively analyzed. The proposed models corresponding to the optimal weights result in the least mean square error (MSE) for all the system states. Further, the MSE for the proposed model is less in most of the oscillators compared with the one reported in the literature. The proposed prediction model’s out-of-sample forecasting plots show the best tracking ability to approximate future state values.

Forecasting Models for Chaotic Fractional–Order Oscillators Using Neural Networks

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This paper proposes novel forecasting models for fractional-order chaotic oscillators, such as Duffing’s, Van der Pol’s, Tamaševičius’s and Chua’s, using...

Forecasting Models for Chaotic Fractional–Order Oscillators Using Neural Networks

Published Online: Sep 27, 2021

Page range: 387 - 398

Received: Mar 17, 2021

Accepted: Jul 06, 2021

DOI: https://doi.org/10.34768/amcs-2021-0026

Keywords
chaotic oscillators, data-driven forecasting, fractional-order systems, model-free analysis, neural networks, time-series prediction

© 2021 Kishore Bingi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Forecasting Models for Chaotic Fractional–Order Oscillators Using Neural Networks

Published Online: Sep 27, 2021

Page range: 387 - 398

Received: Mar 17, 2021

Accepted: Jul 06, 2021

DOI: https://doi.org/10.34768/amcs-2021-0026

Keywordschaotic oscillators, data-driven forecasting, fractional-order systems, model-free analysis, neural networks, time-series prediction

© 2021 Kishore Bingi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
chaotic oscillators, data-driven forecasting, fractional-order systems, model-free analysis, neural networks, time-series prediction