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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Almost Periodic Solutions of Recurrent Neural Networks with State-Dependent and Structured Impulses

Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 141--165 | DOI:10.5890/DNC.2023.03.011

Marat Akhmet, G\"{u}lbahar Erim

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Abstract

The subject of the present paper is recurrent neural networks with variable impulsive moments. The impact activation functions are specified such that the structure for the jump equations are in full accordance with that one for the differential equation. The system studied in this paper covers the works done before, not only because the impacts have recurrent form, but also impulses are not state-dependent. The conditions for existence and uniqueness of asymptotically stable discontinuous almost periodic solutions are obtained. Through the present study, the possibility of neuron membranes with negative capacitance is involved in neural networks and this is one of the main novelties of the present study. The vector-matrix representation of the system is used for the clarity of the proofs and for making calculations easier.

Acknowledgments

The authors wish to express their sincere gratitude to the reviewers for the helpful criticism and valuable suggestions, which helped to improve the paper. The first author is supported by $2247-A$ National Leading Researchers Program of TUBITAK, Turkey, N 120C138.

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