Solutions of the BCM learning rule in a network of lateral interacting nonlinear neurons.

We introduce a new method for obtaining the fixed points for neurons that follow the BCM learning rule. The new formalism, which is based on the objective function formulation, permits analysis of a laterally connected network of nonlinear neurons and allows explicit calculation of the fixed points under various network conditions. We show that the stable fixed points, in terms of the postsynaptic activity, are not altered by the lateral connectivity or nonlinearity. We show that the lateral connectivity alters the probability of attaining different states in a network of interacting neurons. We further show the exact alteration in presynaptic weights as a result of the neuronal nonlinearity.