Evolution Properties of Complex-Valued Memristive Differential-Algebraic Neural Networks

Abstract

The study of differential-algebraic neural network is a new and fascinating field. In this paper, one kind of novel mathematical expression combining differential equation and algebraic equation is designed. Some sufficient conditions are presented via the mean value theorem of multi-valued differentials and the control theory of differential systems to ensure global asymptotic stability of complex-valued memristive differential-algebraic neural networks. Several criteria are given to assure that a unique equilibrium point of this model is existed, in addition, it is globally asymptotically stable via the properties of nonsingular M-matrices and definitions of stability. It is noteworthy that these conditions are an extension of existing works. Moreover, numerical simulations are given to test theoretical results.