Labyrinth Chaos

Labyrinth Chaos




J. C. Sprott
Department of Physics, University of Wisconsin, 1150 University Ave., Madison, WI 53706, USA

Konstantinos E. Chlouverakis
Department of Informatics and Telecommunications, University of Athens, Athens 15784, Greece

ABSTRACT
A particularly simple and mathematically elegant example of chaos in a three-dimensional flow is examined in detail. It has the property of cyclic symmetry with respect to interchange of the three orthogonal axes, a single bifurcation parameter that governs the damping and the attractor dimension over most of the range 2 to 3 (as well as 0 and 1) and whose limiting value b = 0 gives Hamiltonian chaos, three-dimensional deterministic fractional Brownian motion, and an interesting symbolic dynamic.