Adaptation and contraction theory for the synchronization of complex neural networks

Abstract

In this chapter, we will present two different approaches to solve the problem of synchronizing networks of interacting dynamical systems. The former will be based on making the coupling between agents in the network adaptive and evolving so that synchronization can emerge asymptotically. The latter will be using recent results from contraction theory to give conditions on the node dynamics and the network topology that result into the desired synchronized motion. The theoretical results will be illustrated by means of some representative examples, including networks of neural oscillators.