Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks

For a general n-dimensional nonautonomous and nonlinear differential equation with infinite delay, we give sufficient conditions for its global asymptotic stability. The main stability criterion depends on the size of the delay on the linear part and the dominance of the linear terms over the nonlinear terms. We apply our main result to answer several open problems left by Berezansky et al. (2014). Using the obtained theoretical stability results, we get sufficient conditions for both the global asymptotic and global exponential stability of a bidirectional associative memory neural network model with delays which generalizes models recently studied. Finally, a numerical example is given to illustrate the novelty of our results.