On fundamental bifurcations from a hysteresis hyperchaos generator

Author

Suzuki, Takashi ; Saito, Toshimichi

Author_Institution

Olympus Opt. Co. Ltd., Tokyo, Japan

Volume

41

Issue

12

fYear

1994

fDate

12/1/1994 12:00:00 AM

Firstpage

876

Lastpage

884

Abstract

In this paper we discuss a four-dimensional autonomous circuit which includes one hysteresis element. This circuit is governed by two symmetric three dimensional linear equations which are connected to each other by hysteresis switchings. Then we can derive the two-dimensional return map and show the following novel results: 1) Fundamental bifurcation diagram from periodic attractor to hyperchaos. It includes coexistence of torus and periodic attractor; 2) two-parameters bifurcation diagram. It exhibits some regularities for the onset of some periodic attractors and tori; 3) laboratory measurements of the return map attractors; 4) a sufficient condition for the existence of attractors

Keywords

bifurcation; chaos; nonlinear network analysis; piecewise-linear techniques; four-dimensional autonomous circuit; fundamental bifurcations; hysteresis element; hysteresis hyperchaos generator; hysteresis switchings; periodic attractor; return map attractors; symmetric three dimensional linear equations; torus; two-dimensional return map; Bifurcation; Chaos; Circuits; Conductors; Equations; Hysteresis; Laboratories; Piecewise linear techniques; Resistors; Sufficient conditions;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.340849

Filename

340849