Spatiotemporal consequences of relaxation time scales in threshold-coupled systems.

We study a class of models incorporating threshold-activated coupling on a lattice of chaotic elements. In such systems, the relaxation time allowed between chaotic updates determines the intrinsic driving rate due to the local chaos, and we show that there exists an inverse cascade from fixed spatial profiles to spatiotemporal chaos, as the relaxation time grows shorter. We analyze how this spectrum of spatiotemporal transitions arises from the competing time scales of the local chaos and the propagation of coupling.