Analysis of an Immune Network Dynamical System Model with a Small Number of Degrees of Freedom

We numerically study a dynamical system model of an idiotypic immune networkwith a small number of degrees of freedom. The model was originally introducedby Varela et.al., and describes antibodies interacting in a body in order toprepare for the invasion of external antigens. The main purpose of this paper is to investigate the direction of change inthe network system when antigens invade it. We investigate three models,original model, a modified model and a modified model with a threshold ofconcentration over which each antibody can recognize other antibodies. In allthese models, both chaotic and periodic states exist. In particular, we findpeculiar states organized in the network, the clustering state.Comment: 21 pages, 42 figures. All figures are gif format