Dynamics and topology of idiotypic networks

Avidan U. Neumann, Gérard Weisbuch

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Jerne's idiotypic network was previously modelled using simple proliferation dynamics and a homogeneous tree as a connection structure. The present paper studies analytically and numerically the genericity of the previous results when the network connection structure is randomized, e.g. with loops and varying connection intensities. The main feature of the dynamics is the existence of different localized attractors that can be interpreted in terms of vaccination and tolerance. This feature is preserved when loops are added to the network, with a few exceptions concerning some regular lattices. Localized attractors might be destroyed by the introduction of a continuous distribution of connection intensities. We conclude by discussing possible modifications of the elementary model that preserve localization of the attractors and functionality of the network.

Original languageEnglish
Pages (from-to)699-726
Number of pages28
JournalBulletin of Mathematical Biology
Issue number5
StatePublished - Sep 1992
Externally publishedYes

Bibliographical note

Funding Information:
We thank Alan Perelson and Rob DeBoer for enlightening discussions. Grind (DeBoer, 1983) software was used to numerically solve the differential equations. The Laboratoire de Physique Statistique is associated with CNRS (URA 1306) and we acknowledge financial support from Inserm grant 879002. AUN is supported by an Inserm Fellowship.


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