QUALITATIVE BEHAVIOR AND STABILITY OF SOLUTIONS OF A HYBRID SYSTEM

2005 ◽  
Vol 03 (01) ◽  
pp. 17-25 ◽  
Author(s):  
GEORGE SEIFERT
Keyword(s):  
Delay Differential Equations ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Qualitative Behavior ◽  
Dimensional System ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
General Systems ◽  
Two Dimensional System ◽  
Delay Differential

In this paper we consider a certain two-dimensional system of delay differential equations with piecewise constant arguments. We find conditions under which this system has constant solutions; i.e. equilibrium points, and their behavior and stability properties. We also find conditions under which certain of these solutions have a type of chaotic behavior. This paper contains results for more general systems than were dealt with in a previous paper [9].

scholarly journals On approximation of the solutions of delay differential equations by using piecewise constant arguments

1991 ◽  
Vol 14 (1) ◽  
pp. 111-126 ◽  
Author(s):  
Istevan Györi
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Difference Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Neutral Type ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Delay Differential

By using the Gronwall Bellman inequality we prove some limit relations between the solutions of delay differential equations with continuous arguments and the solutions of some related delay differential equations with piecewise constant arguments(EPCA).EPCAare strongly related to some discrete difference equations arising in numerical analysis, therefore the results can be used to compute numerical solutions of delay differential equations. We also consider the delay differential equations of neutral type by applying a generalization of the Gronwall Bellman inequality.

scholarly journals Existence conditions for periodic solutions of second-order neutral delay differential equations with piecewise constant arguments

2020 ◽  
Vol 18 (1) ◽  
pp. 93-105
Author(s):  
Mukhiddin I. Muminov ◽  
Ali H. M. Murid
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Second Order ◽  
Algebraic Equations ◽  
Neutral Delay ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Abstract In this paper, we describe a method to solve the problem of finding periodic solutions for second-order neutral delay-differential equations with piecewise constant arguments of the form x″(t) + px″(t − 1) = qx([t]) + f(t), where [⋅] denotes the greatest integer function, p and q are nonzero real or complex constants, and f(t) is complex valued periodic function. The method reduces the problem to a system of algebraic equations. We give explicit formula for the solutions of the equation. We also give counter examples to some previous findings concerning uniqueness of solution.

scholarly journals New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1159
Author(s):  
Shyam Sundar Santra ◽  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Fluid Dynamics ◽  
Neural Networks ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Qualitative Behavior ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Delay Differential

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

scholarly journals On a class of third order neutral delay differential equations with piecewise constant argument

1994 ◽  
Vol 17 (1) ◽  
pp. 113-117 ◽  
Author(s):  
Garyfalos Papaschinopoulos
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Constant Argument

In this paper we study existence, uniqueness and asymptotic stability of the solutions of a class of third order neutral delay differential equations with piecewise constant argument.

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