Using synchronism of chaos for adaptive learning of network topology

In this paper we consider networks of dynamical systems that evolve in synchrony and investigate how dynamical information from the synchronization dynamics can be effectively used to learn the network topology, i.e., identify the time evolution of the couplings between the network nodes. To this aim, we present an adaptive strategy that, based on a potential that the network systems seek to minimize in order to maintain synchronization, can be successfully applied to identify the time evolution of the network from limited information. This strategy takes advantage of the properties of synchronism of chaos and of the presence of different communication delays over the network links. As a motivating example we consider a network of sensors surveying an area, in which information regarding the time evolution of the network connections can be used, e.g., to detect changes taking place within the area. We propose two different setups for our strategy. In the first one, synchronization has to be achieved at each node (as well as the identification of the couplings over the network links), based solely on a single scalar signal representing a superposition of signals from the other nodes in the network. In the second one, we incorporate an additional node, termed the maestro, having the function of maintaining network synchronization. We will see that when such an arrangement is realized, it will become possible to effectively identify the time evolution of networks that are much larger than would be possible in the absence of a maestro.