  We study a dynamical system model of an idiotypic immune network with a small
number of degrees of freedom, mainly focusing on the effect of a threshold
above which antibodies can recognise antibodies. The response of the system to
invasions by antigens is investigated in the both models with and without the
threshold and it turns out that the system changes in a desirable direction for
moderate magnitude of perturbation. direction for moderate magnitude of
perturbation. Also, the propagation of disturbance by an antigen is
investigated in the system of one-dimensionally connected basic units taking
the closed 3-clone system as a unit, and it is clarified that the threshold of
the system has effects to enhance the stability of the network and to localise
the immune response.
