  In this paper we review the trajectory of a model proposed by Stauffer and
Weisbuch in 1992 to describe the evolution of the immune repertoire and present
new results about its dynamical behavior. Ten years later this model, which is
based on the ideas of the immune network as proposed by Jerne, has been able to
describe a multi-connected network and could be used to reproduce immunization
and aging experiments performed with mice. Besides its biological implications,
the physical aspects of the complex dynamics of this network is very
interesting {\it per se}. The immunization protocol is simulated by introducing
small and large perturbations (damages), and in this work we discuss the role
of both. In a very recent paper we studied the aging effects by using
auto-correlation functions, and the results obtained apparently indicated that
the small perturbations would be more important than the large ones, since
their cumulative effects may change the attractor of the dynamics. However our
new results indicate that both types of perturbations are important. It is the
cooperative effects between both that lead to the complex behavior which allows
to reproduce experimental results.
