Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2000-06-25
Nonlinear Sciences
Adaptation and Self-Organizing Systems
35 pages, 14 pages
Scientific paper
We study the emergence of the collective spatio-temporal macroscopic properties of the immune system, by representing individually the elementary interactions between its microscopic components (antibodies, antigens, cytokines). The results of this detailed explicit analysis are compared with the traditional procedure of averaging over individuals and representing the collective dynamics in terms of densities that obey partial differential equations (PDE). The simulations show even for very simple elementary reactions the spontaneous emergence of localized complex structures. In turn the effective dynamics of these structures affects the average behavior of the system in a very decisive way: systems which would according to the differential equations approximation die, display in reality a very lively behavior. Our conclusions are supported both by explicit microscopic simulations and by analytic calculations. As the optimal method we propose a mixture of microscopic simulation (MS) systems describing each reaction separately, and average methods describing the average behavior of the agents.
Atlan Henri
Cohen Irun R.
Louzoun Yoram
Solomon Sorin
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