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

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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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Citation Formats

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.