Abrupt Dimension Changes at Basin Boundary Metamorphoses

B S Park, Celso Grebogi, Ying-Cheng Lai

Research output: Contribution to journalArticlepeer-review


Basin boundaries in chaotic dynamical systems can be either smooth or fractal. As a system parameter changes, the structure of the basin boundary also changes. In particular, the dimension of the basin boundary changes continuously except when a basin boundary metamorphosis occurs, at which it can change abruptly. We present numerical experiments to demonstrate such sudden dimension changes. We have also used a one-dimensional analytic calculation and a two-dimensional qualitative model to explain such changes.
Original languageEnglish
Article number533-541
JournalInternational Journal of Bifurcation and Chaos
Issue number3
Publication statusPublished - Sept 1992


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