On synchronization and consensus patterns in complex networks: from analysis to control

Over the past few years, the study of the mechanisms to achieve consensus and synchronization in complex networks has attracted the interest of the Scientific Community. Most of the results on synchronization and consensus are obtained under the assumption that some form cooperation occurs between the nodes. Unfortunately, this assumption is not satisfied in many instances of systems from Nature and Technology. For example, biochemical and social networks are often characterized by some form of antagonism between nodes. The same happens for complex networked control systems where agents need to optimize conflicting utility functions. In this paper, we present new conditions for the onset of synchronization and consensus patterns in complex networks. Essentially, we show that if network nodes exhibit some symmetry, then this can be potentially translated into a synchronization/consensus pattern, where two groups of nodes emerge. Interestingly, the symmetry at the node level is also reflected at the network level as the trajectories of the two groups are related with each other via this symmetry. We also show that our results can be turned into a design tool and offer a systematic methodology to address the problem of designing a network controller that drives the network towards a desired synchronization/consensus pattern.