Canards and chaos in nonlinear systems

Author

Itoh, Makoto ; Chua, Leon O.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Nagasaki Univ., Japan

Volume

6

fYear

1992

fDate

10-13 May 1992

Firstpage

2789

Abstract

Canards are a new phenomenon in slow-fast systems. The canard phenomenon in three types of nonlinear systems is studied. The authors first study the behavior of the Hopf bifurcation for the following two-dimensional systems: (a) a slow-fast system with a cubic nonlinearity, (b) a system with a constrained curve, and (c) a slow-fast system with a piecewise linear nonlinearity. It is shown that systems (a) and (b) have canard cycles, but the other forgets them. The Hopf bifurcation scheme of the system (a) is continuous, but (b) and (c) are discontinuous. The same questions are considered for three-dimensional systems. The canard with a pseudosingular saddle point is studied, and its role in the system dynamics is explained. It is shown that the slow-fast system with a piecewise linear nonlinearity drops this kind of canard. By using this result, the existence of a chaotic attractor is shown

Keywords

bifurcation; chaos; nonlinear systems; piecewise-linear techniques; Hopf bifurcation; canard phenomenon; chaotic attractor; constrained curve; cubic nonlinearity; nonlinear systems; piecewise linear nonlinearity; pseudosingular saddle point; slow-fast systems; system dynamics; three-dimensional systems; two-dimensional systems; Bifurcation; Chaos; Circuit noise; Differential equations; Laboratories; Nonlinear circuits; Nonlinear dynamical systems; Nonlinear equations; Nonlinear systems; Piecewise linear techniques;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1992. ISCAS '92. Proceedings., 1992 IEEE International Symposium on

Conference_Location

San Diego, CA

Print_ISBN

0-7803-0593-0

Type

conf

DOI

10.1109/ISCAS.1992.230619

Filename

230619