Stability analysis and synthesis algorithm of bidirectional associative memory

In the present paper we investigate the qualitative properties of a class of bidirectional associative memories. Networks are described by a system of first order ordinary difference equations which are defined on a closed hypercube of the state space with solutions extended to the boundary of the hypercube. For the present model, a systematic analysis method is developed to completely characterize a given network, i.e., the distribution of equilibria in the state space, and the stability properties of the equilibrium points. In addition, we establish a computationally efficient synthesis procedure utilizing the eigenstructure decomposition method. The proposed algorithm possesses several advantages, since it is possible to exert control over the number of spurious states, since it is possible to estimate the basins of attraction of the stable memories, and since it is possible, under certain constraints, to effectively store a number of desired stable memories which by far exceed the order of the network. The applicability of the present results is demonstrated by means of a specific application in flexible structures