Unpredictable oscillations for hopfield-type neural networks with delayed and advanced arguments
Akhmet M. Çinçin D.A. Tleubergenova M. Nugayeva Z.
1 March 2021MDPI AG
Mathematics
2021#9Issue 5
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.
Delayed and advanced generalized piecewise constant argument , Exponential stability , Hopfield neural networks , Poincaré chaos , Transmission of chaotic signals , Unpredictable input-output , Unpredictable oscillations
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Department of Mathematics, Middle East Technical University, Ankara, 06800, Turkey
Department of Mathematics, Süleyman Demirel University, Isparta, 32260, Turkey
Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe, 030000, Kazakhstan
Institute of Information and Computational Technologies CS MES RK, Almaty, 050000, Kazakhstan
Department of Mathematics
Department of Mathematics
Department of Mathematics
Institute of Information and Computational Technologies CS MES RK
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