MM-matrix structure and harmless delays in a Hopfield-type neural network

Motivated by work in [W. Ma, T. Hara, Y. Takeuchi, Stability of a 2-dimensional neural network with time delays, J. Biol. Syst. 8 (2000) 177–193; S.A. Campbell, Delay independent stability for additive neural networks, in: New Millennium Special Issue on Neural Networks and Neurocomputing—Theory, Models and Applications Part I, Differential Equations Dynam. Syst. 9 (2001) 115–138; S. Zhang, W. Ma, Y. Kuang, Necessary and sufficient conditions for global attractivity of Hopfield-type neural networks with time delays, Rocky Mountain J. Math. 38 (2008) 1829–1840], this work gives some necessary and sufficient conditions for global attractivity of an nn-dimensional Hopfield-type neural network model with time delays based on the MM-matrix and a class of nonlinear algebra equations with nn variables.