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A Recurrent Neural Network for Identifying Multiple Chaotic Systems

Author

Listed:
  • José Luis Echenausía-Monroy

    (Applied Physics Division, Department of Electronics and Telecommunications, CICESE, Carr. Ensenada-Tijuana 3918, Zona Playitas, Ensenada 22860, Mexico
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

  • 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
    Preparatoria Regional de Lagos de Moreno, Universidad de Guadalajara, Lagos de Moreno 47476, Mexico
    These authors contributed equally to this work.)

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.

Suggested Citation

  • José Luis Echenausía-Monroy & Jonatan Pena Ramirez & Joaquín Álvarez & Raúl Rivera-Rodríguez & Luis Javier Ontañón-García & Daniel Alejandro Magallón-García, 2024. "A Recurrent Neural Network for Identifying Multiple Chaotic Systems," Mathematics, MDPI, vol. 12(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1835-:d:1413943
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    References listed on IDEAS

    as
    1. Daniel A. Magallón & Rider Jaimes-Reátegui & Juan H. García-López & Guillermo Huerta-Cuellar & Didier López-Mancilla & Alexander N. Pisarchik, 2022. "Control of Multistability in an Erbium-Doped Fiber Laser by an Artificial Neural Network: A Numerical Approach," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
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