The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations

Abstract EN

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.