We study bounds on the coupling strengths required to synchronize dynamical systems coupled via undirected and directed complex networks. In particular, we leverage tools from spectral graph theory to derive conditions based on the topological structures of the networks.

Chapter Contents:

• 10.1 Introduction
• 10.2 Network model and preliminaries
• 10.3 Tools of graph comparison
• 10.4 Synchronization in an undirected network
• 10.4.1 Graph comparison with the complete graph
• 10.4.2 Graph comparison with the star graph
• 10.4.3 Illustrative examples
• 10.4.3.1 Benefits from comparing with star graphs
• 10.4.3.2 Applications in dynamic networks with growing topologies
• 10.5 Synchronization in a directed network
• 10.5.1 Graph comparison with the complete graph
• 10.5.2 Illustrative examples
• 10.5.2.1 The directed ring graph
• 10.5.2.2 Graph with three nodes
• 10.6 Conclusions
• Acknowledgments
• Appendix A: Comments on Assumption 10.1
• Appendix B: Numerical simulation
• References

Inspec keywords: complex networks; synchronisation; directed graphs; network theory (graphs)

Other keywords: graph comparison; coupling strength bound; spectral graph theory; graph synchronization; complex networks; topological network structure; directed complex network; undirected complex network; dynamical system synchronization

Subjects: Combinatorial mathematics; Combinatorial mathematics; Algebra, set theory, and graph theory; Combinatorial mathematics