Properties of small neural networks

Networks containing neuronal models of the type considered in the previous paper can be described by a set of first order differential equations. Steady-state solutions and the stability of these solutions to small perturbations can be obtained. Networks of physiological interest which give rise to second, third and fourth order linear equations are analysed in detail. Conditions are derived under which such networks can be condensed into a single neuron of similar order. Simple mechanisms for memory storage, for the generation of oscillatory activity and for decision making in neural systems are suggested.