Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments
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Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey
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Department of Mathematics, Süleyman Demirel University, Isparta 32260, Turkey
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Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
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Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan
*
Author to whom correspondence should be addressed.
Academic Editor: Miguel Atencia
Mathematics 2021, 9(5), 571; https://doi.org/10.3390/math9050571
Received: 9 February 2021
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Revised: 2 March 2021
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Accepted: 4 March 2021
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Published: 7 March 2021
(This article belongs to the Special Issue Numerical Analysis of Artificial Neural Networks)
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.
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Keywords:
hopfield neural networks; unpredictable oscillations; unpredictable input-output; transmission of chaotic signals; delayed and advanced generalized piecewise constant argument; Poincaré chaos; exponential stability
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MDPI and ACS Style
Akhmet, M.; Aruğaslan Çinçin, D.; Tleubergenova, M.; Nugayeva, Z. Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments. Mathematics 2021, 9, 571. https://doi.org/10.3390/math9050571
AMA Style
Akhmet M, Aruğaslan Çinçin D, Tleubergenova M, Nugayeva Z. Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments. Mathematics. 2021; 9(5):571. https://doi.org/10.3390/math9050571
Chicago/Turabian StyleAkhmet, Marat, Duygu Aruğaslan Çinçin, Madina Tleubergenova, and Zakhira Nugayeva. 2021. "Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments" Mathematics 9, no. 5: 571. https://doi.org/10.3390/math9050571
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