Coupled Networks, Patterns and Complexity - Abstract
Atay, Fatihcan
Many natural and man-made systems are intrinsically complex, the human brain being the most complex system known to man. Although it is not realistic to expect to capture the whole scale of this complexity into mathematical and computational models, we might nevertheless hope to understand at least certain aspects through abstract models. One such aspect is Emergence, that is, the question of how novel complex dynamics arise from the interaction of simple units. This talk will study emergence in the context of a particular but important behavior of networked systems, namely synchronization. Complete synchronization refers to the case where all units in the network display identical behavior. On the one hand, synchronization serves to amplify the output signal from the network; on the other hand, the complexity of the system is apparently reduced, since the behavior is now spatially homogeneous. For instance, in diffusively-coupled systems, the synchronized network behaves exactly like the individual isolated units, so no new behavior emerges from synchronization. How can one then reconcile the concepts of synchronization and emergence? I will present two mechanisms as answer. The first mechanism is the presence of time delays in the network and the second one is non-diffusive coupling. In the first case, the units are only aware of a past state of the network, in the second case their interaction is not designed for cooperation. Hence, it is not obvious that such systems can synchronize their actions at all. It surprisingly turns out that both systems can indeed exhibit synchronization under appropriate conditions. Furthermore, the synchronized network can display a rich range of dynamics much different from that of individual units.