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 (2007)

The complete paper is available in PDF format.

See an interactive animation of this system.

Return to Sprott's Books and Publications.