scholarly journals The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhichun Yang
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Delay Differential Equations ◽  
Impulsive System ◽  
Invariant Sets ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential ◽  
New Criteria

This paper is concerned with asymptotical behavior for a class of impulsive delay differential equations. The new criteria for determining attracting sets and attracting basin of the impulsive system are obtained by developing the properties of quasi-invariant sets. Examples and numerical simulations are given to illustrate the effectiveness of our results. In addition, we show that the impulsive effects may play a key role to these asymptotical properties even though the solutions of corresponding nonimpulsive systems are unbounded.

scholarly journals Asymptotic Behavior and Stability in Linear Impulsive Delay Differential Equations with Periodic Coefficients

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1802
Author(s):  
Ali Fuat Yeniçerioğlu ◽  
Vildan Yazıcı ◽  
Cüneyt Yazıcı
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Delay Differential Equations ◽  
Periodic Coefficients ◽  
Special Cases ◽  
Impulsive Delay Differential Equations ◽  
Constant Coefficients ◽  
Impulsive Delay ◽  
Delay Differential

We study first order linear impulsive delay differential equations with periodic coefficients and constant delays. This study presents some new results on the asymptotic behavior and stability. Thus, a proper real root was used for a representative characteristic equation. Applications to special cases, such as linear impulsive delay differential equations with constant coefficients, were also presented. In this study, we gave three different cases (stable, asymptotic stable and unstable) in one example. The findings suggest that an equation that is in a way that characteristic equation plays a crucial role in establishing the results in this study.

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