TOPOLOGICAL PROPERTIES OF CONTINUOUS NEURAL NETWORKS WITH ANALOG NEURONS.

The properties of the neural network are discussed chiefly from the viewpoint of the topological properties of its states. Equilibrium is considered as one of the topological properties. A sufficient condition is shown for the existence of the equilibrium state and, especially, the necessary and sufficient condition is shown for the existence of a uniform equilibrium state. Since a neural network has in general more than one equilibrium state, the maximum number of such states and the region of their existence are discussed. Convergence of successive approximation in determination of the equilibrium state is discussed and a difference is seen between the dynamics of the network states with continuous time and with discrete time.