Hyperlabyrinth Chaos: From Chaotic Walks to Spatiotemporal Chaos
Konstantinos E. Chlouverakis
Department of Informatics and
Telecommunications, University of Athens, Athens 15784, Greece
J. C. Sprott
Departments of Physics, University
of Wisconsin, 1150 University Avenue, Madison, WI 53706, USA
(Received 12 July 2006; accepted 3 September 2007; published online
21 May 2007)
In this paper we examine a very simple and elegant example of
high-dimensional chaos in a coupled array of flows in ring architecture
that is cyclically symmetric and can also be viewed as an N-dimensional spatially infinite
labyrinth (a "hyperlabyrinth"). The scaling laws of the largest
Lyapunov exponent, the Kaplan-Yorke dimension, and the metric entropy
are investigated in the high-dimensional limit (3 < N < 101) together with its
routes to chaos. It is shown that by tuning the single bifurcation
parameter b that governs the
dissipation and the number of coupled systems N, the attractor dimension can span
the entire range of 0 to N
including Hamiltonian (conservative) hyperchaos in the limit of b = 0 and, furthermore,
spatiotemporal chaotic behavior. Finally, stability analysis reveals
interesting and important changes in the dynamics, whether N is even or odd.
Ref: K. E. Chlouverakis and J. C. Sprott,
Chaos 17, 023110-1 - 023110-8
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