Chaos, torus and synchronization from three coupled relaxation oscillators

Author

Saito, Toshimichi ; Matsumoto, Yoshiaki

Author_Institution

Dept. of Electr. Eng., Hosei Univ., Tokyo, Japan

Volume

41

Issue

11

fYear

1994

fDate

11/1/1994 12:00:00 AM

Firstpage

754

Lastpage

759

Abstract

This paper analyzes fundamental phenomena from three coupled relaxation oscillators. The system nonlinearity is a piecewise linear hysteresis comparator and we can explicitly calculate the return map and its Lyapunov exponents. Then we clarify generation of chaos, 2-torus, 3-torus and various kinds of synchronizations. Also, a rough bifurcation diagram is given. It indicates that 3-torus is popular for weak coupling and chaos is popular for relatively strong coupling. Some of the phenomena are confirmed by laboratory measurements

Keywords

bifurcation; chaos; hysteresis; nonlinear network analysis; piecewise-linear techniques; relaxation oscillators; synchronisation; Lyapunov exponents; bifurcation diagram; chaos; coupled relaxation oscillators; piecewise linear hysteresis comparator; return map; synchronization; system nonlinearity; three coupled oscillators; torus; Bifurcation; Chaos; Circuits and systems; Coupling circuits; Frequency synchronization; Hysteresis; Laboratories; Large-scale systems; Oscillators; Piecewise linear techniques;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.331531

Filename

331531