Asymptotic Stability and Polynomial Stability of Impulsive Cohen–Grossberg Neural Networks with Multi-proportional Delays

摘要

This paper is concerned with the global asymptotic stability (GAS) and global polynomial stability (GPS) of impulsive Cohen–Grossberg neural networks (ICGNNs) with multi-proportional delays. The concept of GPS of the ICGNNs considered is first proposed and it is pointed out that the GPS is also one of the dynamics of recurrent neural networks with proportional delays. The GPS criteria depending on proportional delay factors are made by introducing tunable parameters, skillfully designing Lyapunov functionals and using inequality skills. The application scope of the ICGNNs considered parameters is extended by introducing tunable parameters. And the relationship of exponential stability, polynomial stability and asymptotic stability of the ICGNNs considered is revealed. These criteria proposed are checked by two numerical examples and simulations.