Cycling chaos

Author

Dellnitz, Michael ; Field, Michael ; Golubitsky, Martin ; Hohmann, Andreas ; Ma, Jun

Author_Institution

Inst. fur Angewandte Math., Hamburg Univ., Germany

Volume

42

Issue

10

fYear

1995

fDate

10/1/1995 12:00:00 AM

Firstpage

821

Lastpage

823

Abstract

Saddle connections between equilibria can occur structurally stable in systems with symmetry, and these saddle connections can cycle so that a given equilibrium is connected to itself by a sequence of connections. These cycles provide a way of generating intermittency, as a trajectory will spend some time near each saddle before quickly moving to the next saddle. Guckenheime and Holmes (1988) showed that cycles of saddle connections can appear via bifurcation. In this paper, we show numerically that the equilibria in the Guckenheimer-Holmes example can be replaced by chaotic sets, such as those that appear in a Chua circuit or a Lorenz attractor. Consequently, there are trajectories that behave chaotically, but where the spatial location of the chaos cycles. We call this phenomenon cycling chaos

Keywords

Chua´s circuit; Lorentz transformation; chaos; differential equations; Chua circuit; Guckenheimer-Holmes example; Lorenz attractor; chaotic sets; cycling chaos; intermittency; ordinary differential equations; saddle connections; spatial location; trajectory; Bifurcation; Chaos; Coupling circuits; Differential equations; Limit-cycles; Mathematical model; Nonlinear dynamical systems; Stability;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.473592

Filename

473592