Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments

Marat Akhmet, Duygu Aruğaslan Çinçin, Madina Tleubergenova and Zakhira Nugayeva
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Marat Akhmet: Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey
Duygu Aruğaslan Çinçin: Department of Mathematics, Süleyman Demirel University, Isparta 32260, Turkey
Madina Tleubergenova: Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
Zakhira Nugayeva: Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan

Mathematics, 2021, vol. 9, issue 5, 1-19

Abstract: This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of the unique unpredictable oscillation are proven. According to the theory, the presence of unpredictable oscillations is strong evidence for Poincaré chaos. Consequently, the paper is a contribution to chaos applications in neuroscience. The model is inspired by chaotic time-varying stimuli, which allow studying the distribution of chaotic signals in neural networks. Unpredictable inputs create an excitation wave of neurons that transmit chaotic signals. The technique of analysis includes the ideas used for differential equations with a piecewise constant argument. The results are illustrated by examples and simulations. They are carried out in MATLAB Simulink to demonstrate the simplicity of the diagrammatic approaches.

Keywords: hopfield neural networks; unpredictable oscillations; unpredictable input-output; transmission of chaotic signals; delayed and advanced generalized piecewise constant argument; Poincaré chaos; exponential stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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