A formalism based on window automata is proposed as a method to analyse complex population dynamics. The method is applied to a model of the immune network (Weisbuch, G. et al., 1990. J. theor. Biol. 146, 483-499), and used to predict which attractor the system reaches after antigenic stimulation, as a function of the parameters. The attractors of the dynamics are interpreted in terms of immune conditions such as vaccination or tolerance. Scaling laws that define the regimes in the parameter space corresponding to the specific attractor reached under antigenic stimulation are derived.
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The Laboratoire de Physique Statistique is associated with CNRS (URA 1306) and we acknowledge financial support from Inserm grant 879002. AUN is supported by a Chateaubriand Fellowship.