Affiliation:
1. Laboratoire de Génétique des Procaryotes and Center for Nonlinear Phenomena and Complex Systems, Université de Bruxelles, Bruxelles
Abstract
This paper aims to show how complex nonlinear dynamic systems can be classified, analyzed and synthesized in terms of feedback circuits. The Rössler equations for deterministic chaos are revisited and generalized in this perspective. It is shown that once a proper set of feedback circuits is present in the Jacobian matrix of the system, the chaotic character of trajectories is remarkably robust versus changes in the nature of the nonlinearities. "Labyrinth chaos", whereby simple differential systems generate large lattices of many unstable steady states embedded in a chaotic attractor, is constructed using this technique. In the limit case of a single three-element circuit without diagonal elements, one finds systems possessing an infinite lattice of unstable steady states between which trajectories percolate in a deterministic chaotic way.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)
Cited by
115 articles.
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