Synchronization in Arrays of Chaotic Circuits Coupled via Dynamic Coupling Elements

We study synchronization in arrays of chaotic circuits which are coupled via dynamic coupling elements which can themselves possess chaotic dynamics. We express the synchronization conditions in terms of properties of the underlying hypergraphs and present a result which suggests that under suitable conditions, the more connected the hypergraph is, the easier it is to synchronize the array. The special case of an array of two chaotic circuits is considered. We show that in some cases not all chaotic circuits are synchronized with each other, but clusters are formed in which circuits within a cluster are synchronized to each other.