Unpredictable solutions of quasilinear differential equations with generalized piecewise constant arguments of mixed type

Date

2023-01-01

Author

Tleubergenova, Madina
Çinçin, Duygu Aruğaslan
Nugayeva, Zakhira
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

195
views

0
downloads

An unpredictable solution is found for a quasilinear differential equation with generalized piece-wise constant argument (EPCAG). Sufficient conditions are provided for the existence, uniqueness and exponential stability of the unpredictable solution. The theoretical results are confirmed by examples and illustrated by simulations.

Subject Keywords

delayed and advanced argument, exponential stability, piecewise constant argument of generalized type, Poincaré chaos, quasilinear differential equation, unpredictable solution

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85144134210&origin=inward
https://hdl.handle.net/11511/101592

Journal

Carpathian Journal of Mathematics

DOI

https://doi.org/10.37193/CJM.2023.01.18

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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.
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...
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 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.
Unpredictable solutions of linear differential and discrete equations Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2019-01-01) The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincare chaos. Simulations illustrating the chaos are provided.

Citation Formats

M. Tleubergenova, D. A. Çinçin, Z. Nugayeva, and M. Akhmet, “Unpredictable solutions of quasilinear differential equations with generalized piecewise constant arguments of mixed type,” Carpathian Journal of Mathematics, vol. 39, no. 1, pp. 265–280, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85144134210&origin=inward.