LYAPUNOV-RAZUMIKHIN METHOD FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

Date

2009-10-01

Author

Akhmet, Marat

Metadata

Show full item record

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

Item Usage Stats

126
views

0
downloads

At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.

Subject Keywords

Differential equations with piecewise constant argument of generalized type, Lyapunov's second method, Razumikhin technique, Logistic equation

URI

https://hdl.handle.net/11511/39339

Journal

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

DOI

https://doi.org/10.3934/dcds.2009.25.457

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Method of Lyapunov functions for differential equations with piecewise constant delay Akhmet, Marat; ARUĞASLAN ÇİNÇİN, Duygu; Yılmaz, Elanur (2011-06-15) We address differential equations with piecewise constant argument of generalized type [5-8] and investigate their stability with the second Lyapunov method. Despite the fact that these equations include delay, stability conditions are merely given in terms of Lyapunov functions; that is, no functionals are used. Several examples, one of which considers the logistic equation, are discussed to illustrate the development of the theory. Some of the results were announced at the 14th International Congress on C...
Lyapunov-type inequalities for nonlinear impulsive systems with applications Kayar, Zeynep; Zafer, Agacik (University of Szeged, 2016) We obtain new Lyapunov-type inequalities for systems of nonlinear impulsive differential equations, special cases of which include the impulsive Emden-Fowler equations and half-linear equations. By applying these inequalities, sufficient conditions are derived for the disconjugacy of solutions and the boundedness of weakly oscillatory solutions.
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.
Stability in cellular neural networks with a piecewise constant argument Akhmet, Marat; Yılmaz, Elanur (2010-03-01) In this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1-4], a model of cellular neural networks (CNNs) [5,6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results.
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...

Citation Formats

M. Akhmet, “LYAPUNOV-RAZUMIKHIN METHOD FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT,” DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, pp. 457–466, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39339.