Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics

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AKHMET M., Tleubergenova M., Zhamanshin A.

Chaos, Solitons and Fractals, vol.178, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 178
  • Publication Date: 2024
  • Doi Number: 10.1016/j.chaos.2023.114307
  • Journal Name: Chaos, Solitons and Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Keywords: Cohen-Grossberg neural networks, Compartmental periodic unpredictable inputs and strengths of connectivity, Exponential stability, Numerical simulations, Unpredictable and Poisson stable inputs and strengths of connectivity, Unpredictable and Poisson stable outputs
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we provide theoretical as well as numerical results concerning recurrent oscillations in Cohen-Grossberg neural networks with variable inputs and strengths of connectivity for cells, which are unpredictable or Poisson stable functions. A special case of the compartmental coefficients with periodic and unpredictable ingredients is also carefully researched. By numerical and graphical analysis, it is shown how a constructive technical characteristic, the degree of periodicity, reflects contributions of the ingredients to final outputs of the neural networks. Sufficient conditions are obtained to guarantee the existence of exponentially stable unpredictable outputs of the models. They are specified for Poisson stability by utilizing the original method of included intervals. Examples with numerical simulations that support the theoretical results are provided.