Differential Equations on a Network

Katy Bold kbold@cut.this.part.princeton.edu

Aric Hagberg hagberg@cut.this.part.lanl.gov

Pieter Swart swart@cut.this.part.lanl.gov

We study networks using the dynamics of differential equations to identify key structural features. For example, bistable reaction-diffusion equation dynamics on a network allow one to distinguish between small groups of highly connected nodes and larger groups of highly connected nodes. This work provides fundamental insights into how network structure affects network dynamics and suggests novel algorithms to compute structural properties of networks.