Sustained Oscillations in a Symmetric Cooperative-Competitive Neural Network: Disproof of a Conjecture about Content Addressable Memory,

摘要

Cohen and Grossberg proved that a large class of neural networks with symmetric interaction coefficients admit a global Liapunov function guaranteeing that their trajectories approach equilibrium points. Such networks function as content-addressable memories, and the equilibria are the stored memories. Cohen and Grossberg also conjectured, based upon substantial computational evidence, that networks within a class of mixed cooperative-competitive networks with symmetric interaction coefficients also have this property. This conjecture is here disproved. In particular, a class of homogeneous, distance-dependent, on-center off-surround neural networks are constructed which supports persistent oscillations for appropriate initial data. Such a class is constructed in each even dimension. Similarly systems which have been used to model the dynamics of the hippocampus, are compared to this class of networks to clarify the origins of oscillatory class of behavior in this class of systems. Reprints. (JHD)