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4:00 pm Wednesday, August 28, 2013 Geometry-Analysis Seminar: Dynamics on Asynchronous Networksby Michael Field (Rice University) in HB 227- A complex system in science and technology can often be represented as a network of interacting subsystems or subnetworks. If we follow a reductionist approach, it is natural (though not always reasonable!) to attempt to describe the dynamics of the network in terms of the dynamics of the subsystems of the network. Put another way, we often have a reasonable understanding of the "pieces", but how do they fit together, and what do they do collectively? In the simplest, and most studied cases, the subnetworks all run on the same clock (are updated simultaneously), and dynamics is governed by a fixed set of (usually analytic) dynamical equations: we say the network is synchronous (this is classical dynamics). In biology, especially neuroscience, and technology, for example large distributed systems, these assumptions may not hold: components may run on different clocks, there may be switching between different dynamical equations, and most significantly, and quite unlike what happens in a classical synchronous network, component parts of the network may run independently of the rest of the network, and even stop, for periods of time. We say networks of this type are asynchronous. It is a major challenge to develop the mathematical theory of dynamics on asynchronous networks. In this introductory talk, we describe examples of dynamics on synchronous and asynchronous networks and point out how properties such as switching are forced by an asynchronous structure. We also briefly indicate a relationship with random dynamical systems.
Submitted by hardt@rice.edu |