Basin explosions and escape phenomena in the twin-well Duffing oscillator: compound global bifurcations organizing behaviour
Open Access
- 16 July 1990
- journal article
- Published by The Royal Society in Philosophical Transactions A
- Vol. 332 (1624) , 169-186
- https://doi.org/10.1098/rsta.1990.0107
Abstract
The sinusoidally drive, twin-well Duffing oscillator has become a central archetypal model for studies of chaos and fractal basin boundaries in the nonlinear dynamics of dissipative ordinary differential equations. It can also be used to illustrate and elucidate universal features of the escape from a potential well, the jumps from one-well to cross-well motions displaying similar characteristics to those recently charted for the cubic one-well potential. We identify here some new codimension-two global bifurcations which serve to organize the bifurcation set and structure the related basin explosions and escape phenomena.Keywords
This publication has 13 references indexed in Scilit:
- Fractal control boundaries of driven oscillators and their relevance to safe engineering designProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1990
- Integrity measures quantifying the erosion of smooth and fractal basins of attractionJournal of Sound and Vibration, 1989
- Basins of attraction in driven dynamical systemsPhysical Review A, 1989
- Chaotic phenomena triggering the escape from a potential wellProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1989
- Basin boundary metamorphoses: Changes in accessible boundary orbitsPhysica D: Nonlinear Phenomena, 1987
- Fractal basin boundariesPhysica D: Nonlinear Phenomena, 1985
- Fractal Basin Boundaries and Homoclinic Orbits for Periodic Motion in a Two-Well PotentialPhysical Review Letters, 1985
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector FieldsPublished by Springer Nature ,1983
- An equation for continuous chaosPhysics Letters A, 1976
- ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. IMathematics of the USSR-Sbornik, 1972