Bifurcation structure of the nonautonomous quadratic map
- 1 August 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 32 (2) , 1076-1081
- https://doi.org/10.1103/physreva.32.1076
Abstract
The change in the bifurcation structure of a quadratic map due to the introduction of linear time dependence of the bifurcation parameter is investigated. Although nontrivial fixed points do not exist for this system, a bifurcation diagram can be constructed provided the sweep rate is not too large. The characteristic scaling features and hysteresis effects exhibited in this diagram are studied. Since studies of bifurcation points are often carried out by such parameter variations, the results should provide guides for the interpretation of experimental data.Keywords
This publication has 9 references indexed in Scilit:
- Observation of order and chaos in a nuclear spin–flip laserJournal of the Optical Society of America B, 1985
- Coexisting attractors in a laser with an injected signalJournal of the Optical Society of America B, 1985
- Laser Lorenz Equations with a Time-Dependent ParameterPhysical Review Letters, 1984
- Chaotic behavior of a hybrid optical bistable system without a time delayApplied Physics B Laser and Optics, 1984
- Fluctuations and simple chaotic dynamicsPhysics Reports, 1982
- The universal metric properties of nonlinear transformationsJournal of Statistical Physics, 1979
- Slowly Varying Jump and Transition Phenomena Associated with Algebraic Bifurcation ProblemsSIAM Journal on Applied Mathematics, 1979
- CONTINUOUS CHAOS—FOUR PROTOTYPE EQUATIONSAnnals of the New York Academy of Sciences, 1979
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978