Dynamics of Networks: Theory and Applications (Discrete Mathematics and Its Applications)

This multidisciplinary, self-contained reference deals with dynamical processes in networked systems. After introducing the basic concepts and definitions of dynamical systems, the author establishes the algebraic background needed to understand dynamical processes on networks. He then examines models of dynamical processes on networks, the analysis of consensus models, the analysis of synchronization in real networked systems, the replicator-mutator model in networked systems, epidemic models, and social network models. The book also discusses the necessity of extending current models to include nonrandom long-range interactions.