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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Generation of Synchronous Unpredictable Oscillations by Coupled Hopfield Neural Networks

Journal of Applied Nonlinear Dynamics 13(3) (2024) 591--602 | DOI:10.5890/JAND.2024.09.014

Mehmet Onur Fen$^{1}$, Fatma Tokmak Fen$^{2}$

$^{1}$ Department of Mathematics, TED University, 06420 Ankara, Turkey

$^{2}$ Department of Mathematics, Gazi University, 06560 Ankara, Turkey

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Abstract

A criterion based on generalized synchronization is provided for the extension of unpredictable oscillations among coupled Hopfield neural networks (HNNs). It is shown that if the drive network possesses an unpredictable oscillation, then the same is true for the response network provided that they are synchronized in the generalized sense. Extension of unpredictability in coupled 4D HNNs is exemplified with simulations. The auxiliary system approach and conditional Lyapunov exponents are utilized to demonstrate the presence of synchronization.

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