Refined qualitative analysis for a class of neural networks

New results of qualitative analysis are presented for a class of neural networks (Hopfield-type), representing a refinement in the interpretation of their behaviour. The main instrument of this analysis consists in the individual monitoring of the state-trajectories by considering time-dependent rectangular sets that are forward invariant with respect to the dynamics of the investigated systems. Particular requirements for the rectangular sets approaching the equilibrium point allow a componentwise exploration of the stability properties, offering additional information with respect to the traditional framework (that expresses a global knowledge, built in terms of norms).