Synchronization In Arrays of Chaotic Circuits Coupled via Hypergraphs: Static and Dynamic Coupling

When an array of circuits is coupled via coupling elements which connects two circuits at a time, the underlying coupling topology can be represented as a graph. When the coupling element connects more than two circuits at a time, the underlying coupling topology can be represented as a hypergraph. In this paper, we study the synchronization properties in arrays of chaotic circuits where the underlying coupling topology is a hypergraph. We consider the case where the coupling is due to memoryless (static) components, and the case where the coupling is due to dynamic circuit components. We introduce the algebraic connectivity of a hypergraph and show how it can be used to derive sufficient conditions for synchronization.