Coupled dynamical systems and structure formation

We investigate the formation of structure in coupled dynamical systems. Although the individual elements may possess complex dynamics of their own, the system can globally synchronize. This is even possible when the activities between elements are transmitted with temporal delays, that is, when the system does no longer have an intrinsic notion of simultaneity. For suitable parameter constellations, it can also be observed that the restriction of the individual degrees of freedom of the participating elements caused by the coupling leads to the emergence of global dynamical patterns on a longer time scale. This suggests a new mathematical approach to the formation of structure in coupled systems.