Abstract
The paper considers a general system of ordinary differential equations appearing in the neural network theory. The activation functions are assumed to be continuous and bounded by power type functions of the states and distributed delay terms. These activation functions are not necessarily Lipschitz continuous as it is commonly assumed in the literature. We obtain sufficient conditions for exponential decay of solutions.
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Original Russian Text © N. Tatar, 2017, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2017, No. 4, pp. 72-80.
The author is grateful for the financial support and the facilities provided by King Abdulaziz City of Science and Technology (KACST) under the National Science, Technology and Innovation Plan (NSTIP), Project No. 15-OIL4884-0124.
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Tatar, N. On a general nonlinear problem with distributed delays. J. Contemp. Mathemat. Anal. 52, 184–190 (2017). https://doi.org/10.3103/S1068362317040045
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DOI: https://doi.org/10.3103/S1068362317040045