Impact of global interaction on pattern formation on a disk

Global interaction introduces a new mode of communication among all surface elements and may lead to the formation of a very rich variety of spatiotemporal patterns on a disk some of which cannot exist in its absence. While some of the motions on a disk are analogous to those observed in one-dimensional systems, some, such as targets and spirals, exist only in two-dimensional systems. The global interaction stabilizes motions such as target patterns, which are not stable in its absence. It may, however, destabilize the spiral motion and cause the spiral tip to meander in a rather complex fashion and in some cases to exit the disk. The global interaction also increases the sensitivity of the system to the initial conditions so that qualitatively different patterns may be obtained when different initial conditions are used.