Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument

Date

2018-01-01

Author

Akhmet, Marat
Cengiz, Nur

Metadata

Show full item record

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

Item Usage Stats

167
views

0
downloads

In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/41674

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-1606-138

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Intelligent analysis of chaos roughness in regularity of walk for a two legged robot Kaygisiz, BH; Erkmen, İsmet; Erkmen, Aydan Müşerref (Elsevier BV, 2006-07-01) We describe in this paper a new approach to the identification of the chaotic boundaries of regular (periodic and quasiperiodic) regions in nonlinear systems, using cell mapping equipped with measures of fractal dimension and rough sets. The proposed fractal-rough set approach considers a state space divided into cells where cell trajectories are determined using cell to cell mapping technique. All image cells in the state space, equipped with their individual fractal dimension are then classified as being ...
Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem Dosi (Dosiev), A. A. (IOP Publishing, 2009-11-01) We study the absolute basis problem in algebras of holomorphic functions in non-commuting variables generating a finite-dimensional nilpotent Lie algebra g. This is motivated by J. L. Taylor's programme of non-commutative holomorphic functional calculus in the Lie algebra framework.
Stability criterion for second order linear impulsive differential equations with periodic coefficients Guseinov, G. Sh.; Zafer, Ağacık (Wiley, 2008-01-01) In this paper we obtain instability and stability criteria for second order linear impulsive differential equations with periodic coefficients. Further, a Lyapunov type inequality is also established. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
NONCOMMUTATIVE MACKEY THEOREM Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01) In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
Interval oscillation criteria for second order super-half linear functional differential equations with delay and advanced arguments Zafer, Ağacık (Wiley, 2009-09-01) Sufficient conditions are established for oscillation of second order super half linear equations containing both delay and advanced arguments of the form

Citation Formats

M. Akhmet and N. Cengiz, “Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument,” TURKISH JOURNAL OF MATHEMATICS, pp. 272–292, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41674.