Asymptotic Behavior Analysis Of BAM Quaternion-valued Neural Networks

This paper mainly considers the asymptotic behavior of BAM quaternion-valued neural network.As a special case of BAM neural network,this paper also analyzes the stability of inertial quaternion-valued neural network.Based on the plural decomposition method of quaternion and inequality techniques,some sufficient conditions in complex-valued linear matrix inequality form can be obtained by constructing the appropriate Lyapunov functional.Finally,some numerical simulation examples are given to prove the theoretical conclusion.The full text is summarized as the following five parts:Chapter 1 is the introduction.Firstly,the development of quaternion,the characteristics and properties of BAM neural networks and inertial neural networks are introduced.Then,the research status of dynamic behavior of BAM quaternion-valued neural network is briefly summarized.In Chapter 2,the global dissipativity of a class of BAM quaternion-valued neural networks with time delay is studied.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 BAM quaternion-valued neural networks are decomposed into two complex-valued systems.Using Lyapunov second method and inequality technique,some sufficient conditions in complex-valued linear matrix inequality form are derived to ensure the global dissipativity of the discussed network.In Chapter 3,the Lagrange exponential stability of quaternion-valued inertial neural network with time delay is investigated.Due to the introduction of inertia term,the original system can be transformed into the first-order differential system by constructing a proper variable substitutions.Then,based on the plural decomposition method of quaternion and inequality techniques,some sufficient conditions in complex-valued linear matrix inequality form are derived to ensure the Lagrange exponential stability of the network in question.In the fourth chapter,the stability of the BAM quaternion-valued inertial neural networks with time delay is analyzed.And the stability of the inertial neural network is directly studied in this paper without transforming the inertial terms into first order by some variable substitutions.To avoid the non-commutativity of quaternion multiplication,the BAM quaternion-valued inertial neural networks are equivalently transformed by using the decomposition method of quaternion.And then,by using Lyapunov theory,nonlinearmeasure approach and some inequality techniques,several conditions are derived to ensure the quaternion-valued inertial neural networks globally asymptotically stable and globally exponential stable.The fifth chapter mainly makes a comprehensive summary of the work of the full text,and gives the questions that needs further research,so as to continue to study later.