Strange Nonattracting Chaotic Sets, Crises, and Fluctuating Lyapunov Exponents
- 3 June 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 76 (23) , 4348-4351
- https://doi.org/10.1103/physrevlett.76.4348
Abstract
Chaotic attractors containing periodic orbits with different numbers of unstable directions display fluctuating Lyapunov exponents. We show that the existence of certain nonattracting chaotic sets inside the attractor guarantees the occurrence of this behavior in a persistent manner. These nonattracting sets can be brought inside the attractor via a new type of crisis and may be created, as a parameter is varied, via a sequence of bifurcations out of unstable periodic orbits.Keywords
This publication has 10 references indexed in Scilit:
- Obstructions to Shadowing When a Lyapunov Exponent Fluctuates about ZeroPhysical Review Letters, 1994
- Exploring transient chaos in an NMR-laser experimentPhysical Review Letters, 1994
- Blowout bifurcations: the occurrence of riddled basins and on-off intermittencyPhysics Letters A, 1994
- Scaling behavior of chaotic systems with riddled basinsPhysical Review Letters, 1993
- Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reactionJournal of Nonlinear Science, 1991
- Experimental control of chaosPhysical Review Letters, 1990
- Characterization of an experimental strange attractor by periodic orbitsPhysical Review A, 1989
- Unstable periodic orbits and the dimensions of multifractal chaotic attractorsPhysical Review A, 1988
- Critical exponents for crisis-induced intermittencyPhysical Review A, 1987
- Unstable periodic orbits and the dimension of chaotic attractorsPhysical Review A, 1987