A study of the asymptotic behavior of neural networks

The stability properties are studied of neural networks modeled as a set of nonlinear differential equations of the form TX+X =Wf(X)+b where X is the neural membrane potential vector, W is the network connectivity matrix, and F(X) is the nonlinearity (an essentially sigmoid function). Topologies of neural networks that exhibit asymptotic behavior are established. This behavior depends solely on the topology of the network. Moreover, the connectivity W need not be symmetric. Networks topologically similar to the cerebellum fall in this category and exhibit asymptotic behavior. The simulated behavior of typical neural networks is presented