On the dynamics of a multi-connected network

In this paper, we study the dynamics of a multi-connected network which has been used recently to simulate the evolution of the immune repertoire. In particular, we used this model to reproduce experimental results about immunization and aging performed with mice. Here, we investigate the main features which are responsible for those effects by obtaining the cluster size and the activation time distributions. We observe a power law behavior for the activation time distribution below and at the critical region whereas the cluster size distribution exhibits a characteristic length scale in the biologically relevant region of the parameter space. Only at the transition, we obtain a power law behavior for this distribution. The characteristic cluster size is responsible for the loss of plasticity during the time evolution of the system, leading to aging effects, while the absence of a characteristic time scale in the activation time is associated with memory effects.