On Stability for Non-Instantaneous Impulsive Delay Differential Equations

Many phenomena in nature can be described by establishing differential equation models. To be more practical, we extend the instantaneous impulsive delay differential equations proposed by Faria and Oliveira to the non-instantaneous impulsive delay differential equations. This paper proposes a class of non-instantaneous impulsive delay differential equations which satisfy Yorke-type condition. With the help of the definitions of stability, sufficient conditions for stability and the global asymptotic stability of the zero solution of this model are given. Finally, we give some examples and numerical simulations.