Analyse et synthèse de systèmes à dynamique chaotique en terme de circuits de rétroaction (feedback)

Studies on the biological role of feedback circuits were initially centered on systems with stepwise or steep sigmoidal interactions. It turned out recently that reasoning in terms of feedback circuits (rather than of individual interactions) can be used in a more general context, and, in particular, help understanding the behaviour of weakly nonlinear sys¬ tems «à la Rössler » (with a single nonlinear term) known to generate deterministic chaos. A variety of three-and four-dimensional differential systems displaying a chaotic dynamics have been built. The respective roles of the logical structure (= the network of feedback circuits) and of the nonlinearities — both essential — are discussed.