NARX Prediction of Some Rare Chaotic Flows: Recurrent Fuzzy Functions Approach

Sobhan Goudarzi^a, Sajad Jafari^a, Mohammad Hassan Moradi^a, J. C. Sprott^b

^a Biomedical Engineering Department, Amirkabir Univeresity of Technology, Tehran 15875-4413, Iran

^b Department of Physics. University of Wisconsin - Madison, Madison, WI 53706, USA

Received 24 September 2015
Received in revised form 26 November 2015
Accepted 27 November 2015
Available online 30 November 2015
Communicated by C. R. Doering

ABSTRACT

The nonlinear and dynamic accommodating capability of time domain models makes them a useful representation of chaotic time series for analysis, modeling and prediction. This paper is devoted to the modeling and prediction of chaotic time series with hidden attractors using a nonlinear autoregressive model with exogenous inputs (NARX) based on a novel recurrent fuzzy functions (RFFs) approach. Case studies of recently introduced chaotic systems with hidden attractors plus classical chaotic systems demonstrate that the proposed modeling methodology exhibits better prediction performance from different viewpoints (short term and long term) compared to some other existing methods.