1991•International Journal of Bifurcation and ChaosRequires access

BIFURCATION STRUCTURE OF A DRIVEN, MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR (I): THE SUPERHARMONIC RESONANCE STRUCTURE

F. Kaiser, C. Eichwald

Abstract

Bifurcations in the superharmonic region of a generalized version of the van der Pol oscillator which exhibits three limit cycles are investigated. An external force causes the subsequent breakdown of the self-sustained oscillations. Beyond these series of bifurcations chaotic solutions also exist. In this first part we concentrate on a discussion of the bifurcation structure of the system.

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Key concepts: Van der Pol oscillator, Subharmonic function, Limit cycle, Bifurcation, Chaotic, Limit (mathematics), Mathematics, Series (stratigraphy)