Summary
Chaotic motions in deterministic nonlinear systems are an important topic both from a theoretical and a practical point of view. In particular, there have been many studies of systems which yield bounded nonperiodic trajectories converging to attractors of a rather complicated nature, so-called strange attractors. Their existence was demonstrated in a class of nonlinear oscillators with periodic forcing which occur in electric circuit theory and mechanics. The determination of the domain of attraction of such attractors, depending on the parameters, is an interesting problem. It is shown, that the cell mapping approach, i.e., a discrete version of a Poincaré map, represents a very efficient method for analyzing this problem.
Übersicht
Chaotische Bewegungen in deterministischen nichtlinearen Systemen sind sowohl unter theoretischen als auch praktischen Gesichtspunkten von Bedeutung. Viele Untersuchungen haben sich im besonderen mit Systemen beschäftigt, deren Bewegung durch nichtperiodische Trajektorien gekennzeichnet ist, die zu komplizierten Attraktoren, sogenannten seltsamen Attraktoren, konvergieren. Die Existenz dieser Attraktoren wurde an einer Reihe von nichtlinearen, periodisch erregten Oszillatoren demonstriert, welche in elektrischen Schwingkreisen und der Mechanik auftreten. Die Bestimmung des Einzugsgebietes solcher Attraktoren in Abhängigkeit von den Systemparametern ist ein interessantes Problem. Es wird gezeigt, daß die Zellabbildungsmethode, eine diskrete Version einer Poincaré-Abbildung, ein sehr effizientes Verfahren zur Analyse dieses Problems darstellt.
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Kreuzer, E.J. Analysis of chaotic systems using the cell mapping approach. Ing. arch 55, 285–294 (1985). https://doi.org/10.1007/BF00538223
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DOI: https://doi.org/10.1007/BF00538223