Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System

Z.T. Zhusubaliyev, E.A. Soukhoterin, Erik Mosekilde

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Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border-collision bifurcations. The paper contains a detailed analysis of this type of bifurcational transition in the dynamics of the voltage converter, in particular, the merging and subsequent disappearance of cycles of different types, change of solution type, and period-doubling, -tripling, -quadrupling and -quintupling. We show that a denumerable set of unstable cycles can arise together with stable cycles at border-collision bifurcations. The characteristic peculiarities of border-collision bifurcational transitions in piecewise-smooth systems are described and we provide a comparison with some recent results.
Original languageSpanish
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number12
Pages (from-to)2977-3001
Publication statusPublished - 2002

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