Sequential horseshoe formation in the birth and death of chaotic attractors
- 4 April 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 60 (14) , 1359-1362
- https://doi.org/10.1103/physrevlett.60.1359
Abstract
In periodically driven systems, the intersection of stable and unstable manifolds of saddle orbits forms two distinct (topological) horseshoes: The first horeshoe is associated with the destruction of a chaotic attractor, while the second horseshow creates a new chaotic attractor. A laser model is used to illustrate how sequential horseshoe formation controls the birth and death of chaotic attractors.Keywords
This publication has 12 references indexed in Scilit:
- Laser Chaotic Attractors in CrisisPhysical Review Letters, 1986
- The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$SIAM Journal on Mathematical Analysis, 1985
- Period doubling cascades of attractors: A prerequisite for horseshoesCommunications in Mathematical Physics, 1985
- Bifurcation sequences in horseshoe maps: Infinitely many routes to chaosPhysics Letters A, 1984
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector FieldsPublished by Springer Nature ,1983
- Cascades of period-doubling bifurcations: A prerequisite for horseshoesBulletin of the American Mathematical Society, 1983
- Evidence for Universal Chaotic Behavior of a Driven Nonlinear OscillatorPhysical Review Letters, 1982
- An example of bifurcation to homoclinic orbitsJournal of Differential Equations, 1980
- Averaging and Chaotic Motions in Forced OscillationsSIAM Journal on Applied Mathematics, 1980
- Differentiable dynamical systemsBulletin of the American Mathematical Society, 1967