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

AKHMET M., ARUĞASLAN ÇİNÇİN D., Tleubergenova M., Nugayeva Z.

MATHEMATICS, vol.9, no.5, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.3390/math9050571
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: hopfield neural networks, unpredictable oscillations, unpredictable input-output, transmission of chaotic signals, delayed and advanced generalized piecewise constant argument, Poincar&#233, chaos, exponential stability
  • Middle East Technical University Affiliated: Yes


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 Poincare 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.