Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections, Rates and Inputs

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AKHMET M., Tleubergenova M., Zhamanshin A.

ENTROPY, vol.24, no.11, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 11
  • Publication Date: 2022
  • Doi Number: 10.3390/e24111555
  • Journal Name: ENTROPY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Hopfield-type neural networks, modulo periodic unpredictable synaptic connections, rates and inputs, unpredictable solutions, exponential stability, numerical simulations, EXPONENTIAL STABILITY, GRADED RESPONSE, POINCARE CHAOS, EXISTENCE, SEGMENTATION, OSCILLATION
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.