Uniform approximation of a class of impulsive delayed Hopfield neural networks on the half-line
In this work, we investigate a uniform approximation of a nonautonomous delayed CNN-Hopfield-type impulsive system with an associated impulsive differential system where a partial discretization is introduced with the help of piecewise constant arguments. Sufficient conditions are formulated, which...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2024-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11241 |
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| Summary: | In this work, we investigate a uniform approximation of a nonautonomous delayed CNN-Hopfield-type impulsive system with an associated impulsive differential system where a partial discretization is introduced with the help of piecewise constant arguments. Sufficient conditions are formulated, which imply that the error estimate decays exponentially with time on the half-line $[0,\infty)$. A critical step for the proof of this estimate is to show that, under the assumed conditions, the solutions of the Hopfield impulsive system are exponentially bounded and exponentially stable. A bounded coefficients case is also analyzed under simplified conditions. An example is presented and simulated in order to show the applicability of our conditions. |
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| ISSN: | 1417-3875 |