Global polynomial synchronization of neural networks with bidirectional proportional delays via adaptive pinning control and its application in image encryption.

Abstract

This paper investigates the adaptive global polynomial synchronization (GPS) of neural networks (NNs) with bidirectional proportional delays. By designing an adaptive controller for all node and constructing novel Lyapunov functional, a GPS criterion is derived. To further increase energy efficiency, an adaptive pinning control is also designed and a corresponding GPS criterion is provided. The innovation of this article lies in the design of the controllers that is not directly related to synchronization error, but is related to the activation function. The compression effect of the activation function makes synchronization smoother and can reduce the explosion phenomenon caused by numerical simulations. The obtained criteria are validated through a numerical example and simulations, and one of the synchronization control criteria is applied to image encryption.