On the absolute stability for recurrent neural networks with time delays

In the paper there are considered two main aspects of the analysis for the dynamical properties of the recurrent neural networks with time-delays: the absolute stability and the global qualitative behavior of the system. The first aspect refers to the global asymptotic stability of the zero equilibrium and this means that only a single steady state of the neural network matters (the case of optimizers). The second aspect concerns global behavior of the systems with several equilibria. We have discussed the difficulties and the open problem concerning that second aspect.