Sporadically Fractal Basin Boundaries of Chaotic Systems

Brian R. Hunt; Edward Ott; Epaminondas Rosa, Jr

doi:10.1103/PhysRevLett.82.3597

Sporadically Fractal Basin Boundaries of Chaotic Systems

Brian R. Hunt, Edward Ott, and Epaminondas Rosa, Jr.

Phys. Rev. Lett. 82, 3597 – Published 3 May 1999

Abstract

We demonstrate a new type of basin boundary for typical chaotic dynamical systems. For the case of a two dimensional map, this boundary has the character of the graph of a function that is smooth and differentiable except on a set of fractal dimensions less than one. In spite of the basin boundary being smooth “almost everywhere,” its fractal dimension exceeds one (implying degradation of one's ability to predict the attractor an orbit approaches in the presence of small initial condition uncertainty). We call such a boundary sporadically fractal.

Received 17 November 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.3597

Authors & Affiliations

Brian R. Hunt^* and Edward Ott^†

University of Maryland, College Park, Maryland 20742

Epaminondas Rosa, Jr.

Nonlinear Dynamics Laboratory, Department of Physics, University of Miami, Coral Gables, Florida 33146

^*Department of Mathematics and Institute for Physical Sciences and Technology. Electronic address: bhunt@ipst.umd.edu
^†Institute for Plasma Research, Institute for Systems Research, and Departments of Electrical Engineering and of Physics.