Networks of continuous time open systems
Event details
| Date | 02.06.2015 |
| Hour | 14:15 › 15:30 |
| Speaker | Eugene Lerman (UIUC) |
| Location |
CM 113
|
| Category | Conferences - Seminars |
(This talk is based on collaborations with Lee DeVille and with Dmitry Vagner and David Spivak) Dynamics on networks has been studied from many different points of view. I prefer to think of a complex continuous time system ("a network") as a collection of interacting subsystems. These subsystems are open (i.e., control) systems. There are two rather different aspects of these collections. Given a collection of open systems one can interconnect them to obtain a new open system. The interconnection process can be iterated: collections of open systems obtained by interconnecting smaller open systems can be interconnected again. The iterative aspect of interconnection of open systems is captured well by viewing the collection of all open systems as an algebra over a colored operad. This is an instance of an approach advocated by Spivak. On the other hand one of the fundamental problems in the theory of (closed) dynamical systems is constructing maps between dynamical systems or, failing that, proving their existence. For example, a map from a point to our favorite closed system is an equilibrium, periodic orbits are maps from circles and so on. Thus it is desirable to have a systematic way of constructing maps of dynamical systems out of appropriate maps between collections of open systems. It is these kinds of considerations that underlie the development of the groupoid formalism for coupled cell networks of Golubitsky, Steward and their collaborators and its reinterpretation and extension by DeVille and Lerman. The two considerations/viewpoints suggest that networks of open systems in general should be an algebra over some sort of a double monoidal category. I will outline one such possible construction.
Practical information
- Informed public
- Free
Organizer
- Kathryn Hess