Shunting Inhibitory Cellular Neural Networks with Compartmental Unpredictable Coefficients and Inputs

Marat Akhmet (), Madina Tleubergenova and Akylbek Zhamanshin
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Marat Akhmet: Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey
Madina Tleubergenova: Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan
Akylbek Zhamanshin: Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

Mathematics, 2023, vol. 11, issue 6, 1-18

Abstract: Shunting inhibitory cellular neural networks with compartmental periodic unpredictable coefficients and inputs is the focus of this research. A new algorithm is suggested, to enlarge the set of known unpredictable functions by applying diagonalization in arguments of functions of several variables. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable and Poisson stable outputs are obtained. To attain theoretical results, the included intervals method and the contraction mapping principle are used. Appropriate examples with numerical simulations that support the theoretical results are provided. It is shown how dynamics of the neural network depend on a new numerical characteristic, the degree of periodicity.

Keywords: shunting inhibitory cellular neural networks; compartmental periodic unpredictable functions; unpredictable solutions; Poisson stable solutions; the method of included intervals; exponential stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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