Impulsive Hopfield-type neural network system with piecewise constant argument

Date

2010-08-01

Author

Akhmet, Marat
Yılmaz, Elanur

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

264
views

0
downloads

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.

Subject Keywords

Periodic solutions, Asymptotic stability, Equilibrium, Piecewise constant argument, Hopfield neural networks, Impulsive differential equations

URI

https://hdl.handle.net/11511/31166

Journal

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

DOI

https://doi.org/10.1016/j.nonrwa.2009.09.003

Collections

Graduate School of Social Sciences, Article

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...
Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument Akhmet, Marat; Cengiz, Nur (null; 2015-08-25) 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...
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.
Exponentially dichotomous linear systems of differential equations with piecewise constant argument Akhmet, Marat (2012-01-01) © 2012 L & H Scientific Publishing, LLC.We consider differential equations with piecewise constant argument of generalized type. It is the first time, an attention is given to the exponential dichotomy of linear systems. Bounded, almost periodic and periodic solutions and their stability are discussed. The study is made in such a way that further construction of the theory will follow for ordinary differential equations. The results are illustrated by examples.

Citation Formats

M. Akhmet and E. Yılmaz, “Impulsive Hopfield-type neural network system with piecewise constant argument,” NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, pp. 2584–2593, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31166.