A simple model for the statistics of events in idiotypic networks

A simple random graph model of idiotypic networks is introduced: this model allows (1) to evaluate the stability of the network dynamicsʹ fixed points, and (2) to compute the statistics of events triggered in response to the arrival of new molecules (metadynamics) using a dynamic mean-field approximation based on the theory of branching processes. It is shown that (1) the network dynamics is unlikely to have many stable fixed points in a strict sense, but that (2) the reorganizations which the network undergoes owing to the metadynamics are always subcritical if plausible figures are injected into the model. In other words the distance between successive (unstable or weakly stable) fixed points is relatively small, so that the overall behavior is stable.