How to sync a network?

From flocks of birds to the internet, many of the complex systems that we find in nature or in our daily lives can be modeled as networks. Each element (or node) of a network, in turn, can be a dynamical system, i.e., with its variables evolving over time according to some rule(s). But when connecting dynamical systems in a network, several collective phenomena can manifest. Among these phenomena the complete synchronization (CS) of a network can play an indispensable role in some practical applications, which has led several researchers to investigate, for example, what are the conditions and/or structure of a network that guarantee its synchronization, or how to control a network in order to take it to CS. In this manuscript we will try address these issues by taking Kuramoto model as a starting point, analyzing the stability of its solutions and presenting some results that can help us to understand some dynamic aspects of oscillator networks and to answer the question stated in the title.

Keywords:
Complex systems; network dynamics; synchronization