"Cluster Synchronization of Chaotic Systems in Large Networks"
This event is part of the Condensed Matter Theory Seminar Series.
Synchronization of two chaotic systems is a well-known phenomenon, although it still seems like an oxymoron. But when many oscillators (chaotic or not) are linked together in a network causing them to interact, they can synchronize to other oscillators in the network, but not necessarily all of them. The network can break up into clusters of synchronized systems where the oscillators in the same cluster synchronize, but not to oscillators in other clusters even though all clusters are interconnected and influence each other. I show that such patterns of synchronization can be related to the symmetries of the network. One can use computational group theory to find all the symmetries and hence, clusters. Such symmetries can be huge in number (e.g. 10^66 symmetries in a network of 100 oscillators), but can be found in short time. I'll show how to analyze such systems, determine the stability of the cluster patterns, and find interesting patterns of desynchronization bifurcations. I'll show how one can generate such patterns in an electro-optical system. The methods I present will include the construction of synchronization patterns that do not arise from symmetries, but can be built up from symmetry clusters make symmetries the fundamental concept in many cluster patterns.