Chaos via torus breakdown in the forced van der Pol oscillator

Author

Inaba, Naohiko

Author_Institution

Dept. of Inf. Sci., Utsnomiya Univ., Japan

fYear

1990

fDate

12-14 Aug 1990

Firstpage

1051

Abstract

Chaos in the forced van der Pol oscillator including a pair of diodes is investigated. First, the authors show that the normal forced van der Pol equation exhibits chaos. The generation of chaos is explained by a Lorenz plot. Secondly, they analyze chaos rigorously by using a piecewise-linear technique and a degeneration technique which corresponds to an idealized case where the diode is assumed to operate as an ideal switch. In this case, the Poincare map is derived strictly as one-dimensional mapping which is a noninvertible return mapping of a circle. This mapping clarifies the mechanism of chaos

Keywords

chaos; equivalent circuits; negative resistance; nonlinear network analysis; piecewise-linear techniques; relaxation oscillators; LC oscillator; Lorenz plot; Poincare map; chaos; degeneration technique; forced Rayleigh equation; forced van der Pol oscillator; ideal diode switch; noninvertible return mapping; one-dimensional mapping; piecewise-linear technique; torus breakdown; Chaos; Circuits; Density estimation robust algorithm; Diodes; Electric breakdown; Equations; Piecewise linear approximation; Piecewise linear techniques; Switches; Voltage-controlled oscillators;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1990., Proceedings of the 33rd Midwest Symposium on

Conference_Location

Calgary, Alta.

Print_ISBN

0-7803-0081-5

Type

conf

DOI

10.1109/MWSCAS.1990.140905

Filename

140905