A Recurrent Neural Network for Identifying Multiple Chaotic Systems

José Luis Echenausía-Monroy, Jonatan Pena Ramirez, Joaquín Álvarez (), Raúl Rivera-Rodríguez, Luis Javier Ontañón-García () and Daniel Alejandro Magallón-García ()
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José Luis Echenausía-Monroy: Applied Physics Division, Department of Electronics and Telecommunications, CICESE, Carr. Ensenada-Tijuana 3918, Zona Playitas, Ensenada 22860, Mexico
Jonatan Pena Ramirez: Applied Physics Division, Department of Electronics and Telecommunications, CICESE, Carr. Ensenada-Tijuana 3918, Zona Playitas, Ensenada 22860, Mexico
Joaquín Álvarez: Applied Physics Division, Department of Electronics and Telecommunications, CICESE, Carr. Ensenada-Tijuana 3918, Zona Playitas, Ensenada 22860, Mexico
Raúl Rivera-Rodríguez: Telematics Division, CICESE, Carr. Ensenada-Tijuana 3918, Zona Playitas, Ensenada 22860, Mexico
Luis Javier Ontañón-García: Coordinación Académica Región Altiplano Oeste, Universidad Autónoma de San Luis Potosí, Carretera a Santo Domingo 200, Salinas de Hidalgo 78600, Mexico
Daniel Alejandro Magallón-García: Coordinación Académica Región Altiplano Oeste, Universidad Autónoma de San Luis Potosí, Carretera a Santo Domingo 200, Salinas de Hidalgo 78600, Mexico

Mathematics, 2024, vol. 12, issue 12, 1-13

Abstract: This paper presents a First-Order Recurrent Neural Network activated by a wavelet function, in particular a Morlet wavelet, with a fixed set of parameters and capable of identifying multiple chaotic systems. By maintaining a fixed structure for the neural network and using the same activation function, the network can successfully identify the three state variables of several different chaotic systems, including the Chua, PWL-Rössler, Anishchenko–Astakhov, Álvarez-Curiel, Aizawa, and Rucklidge models. The performance of this approach was validated by numerical simulations in which the accuracy of the state estimation was evaluated using the Mean Square Error (MSE) and the coefficient of determination ( r 2 ), which indicates how well the neural network identifies the behavior of the individual oscillators. In contrast to the methods found in the literature, where a neural network is optimized to identify a single system and its application to another model requires recalibration of the neural algorithm parameters, the proposed model uses a fixed set of parameters to efficiently identify seven chaotic systems. These results build on previously published work by the authors and advance the development of robust and generic neural network structures for the identification of multiple chaotic oscillators.

Keywords: chaos; time series; recurrent neural network; neural network; time series prediction; dynamic systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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