Universal metric properties of an approximate Poincaré map for Duffing's equation with negative stiffness
- 1 March 1983
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 27 (3) , 1700-1701
- https://doi.org/10.1103/physreva.27.1700
Abstract
Recently, Holmes found that the behavior of Duffing's equation with negative stiffness can be studied profitably via its approximate Poincaré section which takes the form of a two-dimensional antisymmetric cubic map. We have pursued the study of its universal metric properties. A renormalization-group calculation shows that its bifurcation ratio is the same as that for the Hénon map. We have also studied the one-dimensional cubic map and found that its bifurcation ratio is the same as the quadratic map, thus answering in the affirmative a recent question raised by May.Keywords
This publication has 11 references indexed in Scilit:
- Period doubling: Universality and critical-point orderPhysical Review A, 1982
- Third-order renormalization-group calculation of the Feigenbaum universal bifurcation ratio in the transition to chaotic behaviorPhysical Review A, 1982
- NONLINEAR PHENOMENA IN ECOLOGY AND EPIDEMIOLOGY*Annals of the New York Academy of Sciences, 1980
- Feigenbaum's ratios of two-dimensional area preserving mapsPhysics Letters A, 1980
- The universal metric properties of nonlinear transformationsJournal of Statistical Physics, 1979
- A nonlinear oscillator with a strange attractorPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1979
- Universal metric properties of bifurcations of endomorphismsJournal of Physics A: General Physics, 1979
- BIFURCATIONS AND DYNAMIC COMPLEXITY IN ECOLOGICAL SYSTEMS*Annals of the New York Academy of Sciences, 1979
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978
- Nonlinear Vibrations of a Buckled Beam Under Harmonic ExcitationJournal of Applied Mechanics, 1971