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ANALYSIS OF TORUS BREAKDOWN INTO CHAOS IN A CONSTRAINT DUFFING VAN DER POL OSCILLATOR

Aihara Complexity Modeling Project, ERATO, JST, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku 153-8505, Japan

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NAOHIKO INABA

Inaba Research Laboratory, 1-45-1 Ekihigashi-dori, Oyama-shi 323-0022, Japan

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TAKASHI TSUBOUCHI

Institute of Engineering Mechanics and Systems, University of Tsukuba, 1-1-1 Ten'noudai, Tsukuba-shi 305-8573, Japan

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KAZUYUKI AIHARA

Institute of Industrial Science, University of Tokyo, Aihara Complexity Modeling Project, ERATO, JST, 4-6-1 Komaba, Meguro-ku 153-8505, Japan

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https://doi.org/10.1142/S0218127408020835Cited by:12 (Source: Crossref)

Abstract

The bifurcation structure of a constraint Duffing van der Pol oscillator with a diode is analyzed and an objective bifurcation diagram is illustrated in detail in this work. An idealized case, where the diode is assumed to operate as a switch, is considered.

In this case, the Poincaré map is constructed as a one-dimensional map: a circle map. The parameter boundary between a torus-generating region where the circle map is a diffeomorphism and a chaos-generating region where the circle map has extrema is derived explicitly, without solving the implicit equations, by adopting some novel ideas. On the bifurcation diagram, intermittency and a saddle-node bifurcation from the periodic state to the quasi-periodic state can be exactly distinguished. Laboratory experiment is also carried out and theoretical results are verified.

Keywords:

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