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Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument
Date
2015-08-25
Author
Akhmet, Marat
Cengiz, Nur
Metadata
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Akhmet [1] generalized differential equations with piecewise constant argument by taking any piecewise constant functions as arguments, and recently he introduced functional dependence on piecewise constant argument [2]. These equations play an important role in applications such as neural networks [3]. In this study, we develope a model of recurrent neural network with functional dependence on piecewise constant argument of generalized type given by x 0 (t) = −Ax (t) + Ex (γ (t)) + Bh (xt) + Cg xγ(t) + D. (1) Using the theoretical results obtained by Akhmet [2], we investigate conditions for exponential stability of periodic solutions for (1).
Subject Keywords
Differential equations with functional dependence on piecewise constant argument
,
Recurrent neural networks
,
Stability
,
Periodic solutions
URI
https://hdl.handle.net/11511/78192
https://acikerisim.bartin.edu.tr/bitstream/handle/11772/1304/ICPAM%202015%20Abstract%20Book%20%28pages%2099-100%29.pdf?sequence=1&isAllowed=y
Conference Name
International Conference on Pure and Applied Mathematics (ICPAM 2015) (25 - 28 Ağustos 2015)
Collections
Department of Mathematics, Conference / Seminar
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M. Akhmet and N. Cengiz, “Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument,” presented at the International Conference on Pure and Applied Mathematics (ICPAM 2015) (25 - 28 Ağustos 2015), Van, Türkiye, 2015, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/78192.