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

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2022-11-01

Author

Akhmet, Marat
Tleubergenova, Madina
Zhamanshin, Akylbek

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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.

Subject 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

URI

https://hdl.handle.net/11511/101804

Journal

ENTROPY

DOI

https://doi.org/10.3390/e24111555

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, M. Tleubergenova, and A. Zhamanshin, “Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections, Rates and Inputs,” ENTROPY, vol. 24, no. 11, pp. 0–0, 2022, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/101804.