Metamorphoses of Basin Boundaries in Nonlinear Dynamical Systems
- 10 March 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 56 (10) , 1011-1014
- https://doi.org/10.1103/physrevlett.56.1011
Abstract
A basin boundary can undergo sudden changes in its character as a system parameter passes through certain critical values. In particular, basin boundaries can suddenly jump in position and can change from being smooth to being fractal. We describe these changes ("metamorphoses") and find that they involve certain special unstable orbits on the basin boundary which are accessible from inside one of the basins. The forced damped pendulum (Josephson junction) is used to illustrate these phenomena.Keywords
This publication has 10 references indexed in Scilit:
- Fractal Basin Boundaries and Homoclinic Orbits for Periodic Motion in a Two-Well PotentialPhysical Review Letters, 1985
- Noise and Chaos in a Fractal Basin Boundary Regime of a Josephson JunctionPhysical Review Letters, 1985
- Fractal basin boundary of a two-dimensional cubic mapPhysics Letters A, 1985
- Intermittent Chaos and Low-Frequency Noise in the Driven Damped PendulumPhysical Review Letters, 1985
- Structure and crises of fractal basin boundariesPhysics Letters A, 1985
- Bistability, basins of attraction and predictability in a forced mass-reaction modelPhysics Letters A, 1984
- Multiple periodic regimes and final state sensitivity in a biochemical systemPhysics Letters A, 1984
- Final state sensitivity: An obstruction to predictabilityPhysics Letters A, 1983
- Fractal Basin Boundaries, Long-Lived Chaotic Transients, and Unstable-Unstable Pair BifurcationPhysical Review Letters, 1983
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector FieldsPublished by Springer Nature ,1983