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

Show full item record

Item Usage Stats

234
views

0
downloads

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

Suggestions

OpenMETU
Core

Global exponential stability of neural networks with non-smooth and impact activations Akhmet, Marat (2012-10-01) In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential s...
Almost periodic solutions of second order neutral differential equations with functional response on piecewise constant argument Akhmet, Marat (2013-01-01) © 2013 L & H Scientific Publishing, LLC.We consider second order functional differential equations with generalized piecewise constant argument. Conditions for existence, uniqueness and stability of Bohr almost periodic solutions are defined. Appropriate examples which illustrate the results are provided.
Stability analysis of recurrent neural networks with piecewise constant argument of generalized type Akhmet, Marat; Yılmaz, Elanur (2010-09-01) In this paper, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of recurrent neural networks (RNNs). The model involves both advanced and delayed arguments. Sufficient conditions are obtained for global exponential stability of the equilibrium point. Examples with numerical simulations are presented to illustrate the results.
Almost periodic solutions of the linear differential equation with piecewise constant argument Akhmet, Marat (2009-10-01) The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Impulsive Hopfield-type neural network system with piecewise constant argument Akhmet, Marat; Yılmaz, Elanur (2010-08-01) In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results.

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.