Epidemic self-synchronization in complex networks

Abstract

In this article we present and evaluate an epidemic algorithm for the synchronization of coupled Kuramoto oscillators in complex network topologies. The algorithm addresses the problem of providing a global, synchronous notion of time in complex, dynamic Peer-to-Peer topologies. For this it requires a periodic coupling of nodes to a single random one-hop-neighbor. The strength of the nodes' couplings is given as a function of the degrees of both coupling partners. We study the emergence of self-synchronization and the resilience against node failures for different coupling strength functions and network topologies. For Watts/Strogatz networks, we observe critical behavior suggesting that small-world properties of the underlying topology are crucial for self-synchronization to occur. From simulations on networks under the effect of churn, we draw the conclusion that special coupling functions can be used to enhance synchronization resilience in power-law Peer-to- Peer topologies. © 2009 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.