Convergence of generalized fuzzy bidirectional associative memory neural networks with thresholds

Based on the fuzzy operator “ν” and a t-norm T, a generalized dynamical model named the fuzzy bidirectional associative memory neural networks (ν -T FBAMs) with thresholds is set up. It shows that every equilibrium of the system is Lyapunov stable if T satisfies Lipschitz condition. It is proved that the existence of the indices of the matrix U, which is the product of the system connection fuzzy matrices, is sufficient condition for the system to be strongly convergent, and the convergence in finite steps of U is sufficient condition for the system to be strongly stable in finite steps. Also we give some stable states and equilibriums of the system by the standard eigenvectors of U.