NUMERICAL BIFURCATION-ANALYSIS OF DISTANCE-DEPENDENT ON-CENTER OFF-SURROUND SHUNTING NEURAL NETWORKS

On-center off-surround shunting neural networks are often applied as m odels for content-addressable memory (CAM), the equilibria being the s tored memories. One important demand of biological plausible CAMs is t hat they function under a broad range of parameters, since several par ameters vary due to postnatal maturation or learning. Ellias, Cohen an d Grossberg have put much effort into showing the stability properties of several configurations of on-center off-surround shunting neural n etworks. In this article we present numerical bifurcation analysis of distance-dependent on-center off-surround shunting neural networks wit h fixed external input. We varied four parameters that may be subject to postnatal maturation: the range of both excitatory and inhibitory c onnections and the strength of both inhibitory and excitatory connecti ons. These analyses show that fold bifurcations occur in the equilibri um behavior of the network by variation of all four parameters. The mo st important result is that the number of activation peaks in the equi librium behavior varies from one to many if the range of inhibitory co nnections is decreased. Moreover, under a broad range of the parameter s the stability of the network is maintained. The examined network is implemented in an ART network, Exact ART, where it functions as the cl assification layer F2. The stability of the ART network with the F2-fi eld in different dynamic regimes is maintained and the behavior is fun ctional in Exact ART. Through a bifurcation the learning behavior of E xact ART may even change from forming local representations to forming distributed representations.