Quasi-synchronization of heterogeneous neural networks with distributed and proportional delays via impulsive control.

• We consider both proportional delay and distributed delay, which are more difficult and need more challenging to calculation than the recent works. • Through designing impulsive controller, several novel sufficient conditions are given and rigorously proved to ensure that the heterogeneous dynamic NNs and the desired trajectory achieve quasi-synchronization. • Using the generalized formula for the variation of proportional delay and distributed delay parameters, the theoretical error bounded of quasi-synchronization is estimated. In this paper, we discuss the quasi-synchronization of delayed heterogeneous dynamic neural networks based on impulsive control. The main difference of this paper with previous works on quasi-synchronization is that both proportional delay and distributed delay are considered. By establishing a novel impulsive delay inequality, combining Lyapunov theory and the concept of average impulsive interval, some necessary items for quasi-synchronization of delayed heterogeneous dynamic neural networks are obtained. Moreover, through using the generalized formulae for the variation of proportional and distributed delay parameters, the theoretical error bounded of quasi-synchronization is estimated. Finally, numerical examples are listed to explain the validity of our results. [ABSTRACT FROM AUTHOR]