Abstract:
The problem of analysis of large-scale networked systems is one of the most interesting current chal- lenges in Dynamical Systems. In this talk, we will present a perspective on this problem that combines an operator-theoretic and graph theoretic approach, but also incorporates, in a strong way, the geometric point of view that is so fruitful in low dimensions. This approach leads to a new proposal for model reduction that is rooted in the dynamics of the system. It also enables analysis of uncertain and stochastic systems - where initial conditions and/or parameter values are not known exactly - within the same framework. Most of the tools apply equally to discontinuous systems. We will motivate the approach by a number of examples, ranging from biomolecular models to power grid systems, that exhibit large scale ("emergent") transitions between states.