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Immune memory can be regarded as an equilibrium state of immune network system with nonlinear dynamical behavior. The rapid response of immune systems to the second-time antigen is owing to the stable structure of memory state forming by a closed idiotypic immune network. Internal image of an antigen is defined while memory state is formed via such network. A dynamical system of cell population based on antibody chains and tree structure is proposed which explains how the memory state is formed in the immune network. [ABSTRACT FROM PUBLISHER]