Stability analysis in Lagrange sense for a class of BAM neural networks of neutral type with multiple time-varying delays

• We discuss Lagrange stability of neutral type BAM neural networks.
• We give the detailed estimations for the globally attractive sets.
• The delays are multi-time-varying bounded or unbounded but not distributed delays.
• The results here generalize and improve the earlier publications.
• The two sufficient conditions of poly-stability in Lagrange sense are also given.

In this paper, Lagrange stability for a class of neutral type BAM neural networks with multiple time-varying and bounded or unbounded delays is studied. Various different types of activation functions are considered, including general bounded and unbounded activation functions. By constructing appropriate Lyapunov functions and applying inequality techniques, some easily verifiable algebraic criteria for the ultimate boundedness and globally attractive sets of neutral type BAM neural networks are obtained. Meanwhile, the estimations of the positive invariant set, globally attractive set and globally exponentially attractive set are given. In particular, the estimations of the globally exponentially attractive sets with respect to the partial variables and the globally attractive sets of the systems are derived. These results here generalize and improve the earlier publications and can be applied to monostable and multistable neural networks as well as chaos control and chaos synchronization. Finally, some examples with numerical simulations are also given to demonstrate our results.