Some Recent Results for Coupled Systems on Networks

Series: 
CDSNS Colloquium
Monday, March 24, 2014 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Univeristy of Alberta
,  
Organizer: 
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.