Global dissipativity of a class of quaternion-valued BAM neural networks with time delay

Abstract

This paper is concerned with the problem of the global dissipativity of a class of quaternion-valued BAM neural networks with time delay. Two different types of activation functions are considered, including general bounded and Lipschitz-type activation functions. Based on the plural decomposition method of quaternion, the quaternion-valued BAM neural network is separated into two complex-valued systems. Using Lyapunov second method and inequality techniques, some sufficient conditions in complex-valued linear matrix inequality form are derived to ensure the global dissipativity of the discussed network. Moreover, the framework of the globally attractive sets are given out as well. Here, the existence and the uniqueness of the equilibrium point needs not to be considered. Finally, two examples are presented and analyzed to illustrate the effectiveness of our theoretical results.