RAPOPORT, Anatol. "Steady States in Random Nets: 1" and "Steady States in Random Nets II", both in The Bulletin of Mathematical Biophysics, December 1948, volume 10, number 4, pp 211-221 and 221-227. Original wrappers, Very good copy. $125
ABSTRACT (for I): A neural net is taken to consist of a semi-infinite chain of neurons with connections distributed according to a certain probability frequency of the lengths of the axones. If an input of excitation is “fed” into the net from an outside source, the statistical properties of the net determine a certain steady state output. The general functional relation between the input and the output is derived as an integral equation. For a certain type of probability distribution of connections, this equation is reducible to a differential equation. The latter can be solved by elementary methods for the output in terms of the input in general and for the input in terms of the output in special cases.
And: ABSTRACT for II: “Two semi-infinite chains are considered interacting as random nets. Conditions for steady state are derived for the cases of cross-excitatory and cross-inhibitory association connections. In the cross-inhibitory case a unique non-trivial self-reproducing steady state is shown to exist. “