Hyperlabyrinth chaos: from chaotic walks to spatiotemporal chaos.

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<or=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.