Consensus and Synchronization in Complex Networks

Many natural systems depend on units falling into step with one another. Fireflies flash together, crickets chirp in rhythm, and an audience claps in unison, driven by visual and acoustic coupling. The same behavior matters for the survival of species, the beating of heart pacemaker cells, epileptic seizures, the firing of neurons in the cat visual cortex, and human cognition.

Distributed systems and networks face a related problem. Often every node, or some of them, must compute a common function of their starting values. A sink node in a sensor network may need the average of all sensor readings, and a group of cooperating agents may need to align their speed and heading. When every node arrives at the same result, the network has reached consensus. Researchers in computational science and engineering use other names for these ideas, including state agreement, rendezvous, and observer design. Getting a small group of expert models of one process to agree is hard, since each model has already been tuned within its own parameter space.

Synchronization and consensus share a mathematical framework across the natural and technical sciences. This book presents the two topics together, so readers can see where they resemble each other and where they differ, both through systematic theory and through practical applications.

The ten chapters are chosen to represent the current research frontier in synchronization and consensus for networked systems. Two of them cover a newer use of synchronization ideas in machine learning. The volume is written for scientists, engineers, graduate students, and practitioners working on synchronization and related phenomena.