Attractor crowding in oscillator arrays

We describe a novel feature of certain arrays of N-coupled nonlinear oscillators. Specifically, the number of stable limit cycles scales as (N-1)! To accomodate this huge multiplicity of attractors, the basins of attraction crowd ever more tightly in phase space with increasing N. Our simulations show that for large enough N, even minute levels of noise cause the system to hop freely among the many coexisting stable attractors.