Georgia Institute of Technology College of Sciences

Many complex models from science and engineering can be studied in the framework of coupled systems of differential equations on networks. A network is given by a directed graph. A local system is defined on each vertex, and directed edges represent couplings among vertex systems. Questions such as stability in the large, synchronization, and complexity in terms of dynamic clusters are of interest. A more recent approach is to investigate the connections between network topology and dynamical behaviours. I will present some recent results on the construction of global Lyapunov functions for coupled systems on networks using a graph theoretic approach, and show how such a construction can help us to establish global behaviours of compelx models.