A dynamical system with a strange attractor and invariant tori
Department of Physics, University of
Wisconsin-Madison, Madison, WI 53706, USA
Received 15 January 2014
Received in revised form 13 March 2014
Accepted 17 March 2014
Available online 21 March 2014
Communicated by C.R. Doering
This paper describes a simple three-dimensional
time-reversible system of ODEs with quadratic nonlinearities and
the unusual property that it exhibits conservative behavior for
some initial conditions and dissipative behavior for others. The
conservative regime has quasi-periodic orbits whose amplitude
depend on the initial conditions, while the dissipative regime
is chaotic. Thus a strange attractor coexists with an infinite
set of nested invariant tori in the state space.
Ref: J. C. Sprott, Phys. Lett. A 378, 1361-1363 (2014)
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Fig. 1. A strange attractor (red) interlinked with a coexisting
invariant torus (green) for System (1).
Fig. 2. A different view of the strange attractor (red)
intertwined with a symmetric repellor (black) and both interlinked
with a coexisting invariant torus (green) for System (1).
Fig. 3. Cross section in the z
= 0 plane showing nested
tori surrounded by a multifractal strange attractor for System
(1). Initial conditions in the conservative region are shown in
blue, and initial conditions in the basin of attraction of the
strange attractor are shown in yellow.