Thursday 5 February 2015

Friday 4 October 2013

2014-2015: Asynchronous networks and event driven dynamics

This reading course deals with topics in dynamical systems at an advanced level, touching upon current frontline research. Each year a selection will be made of material from the area of local bifurcation theory, global bifurcation theory, ergodic theory of dynamical systems or dynamical systems methods for PDEs/FDEs. The selection of reading material will be detailed at the beginning of the academic year.

Theme for  2014-2015: Asynchronous networks and event driven dynamics

Lecture schedule:
Thursday 29 January 2015, 15:00-16:00 in Room 130 (Dynamical Systems Seminar)
Friday 6 February 2015, 10:00-12:00 in Room 642
Friday 13 February 2015, 10:00-12:00 in Room 642

Topics:

1. Motivational questions; models of network dynamics, the reductionist approach and the curse of analyticity.
2. Synchronous networks and limitations of the model –  in theory and practice.
3. Asynchronous networks and event driven dynamics – motivating examples.
4. An example from transport and production.
5. Functional networks, network initialization, deadlocks and network stalls. The factorization of dynamics theorem.
6. Stochastics and numerics.

Summary

Contemporary network problems in engineering, production, transport and computational neuroscience often do not fit well into the classical model of analytic differential equations. Typically nodes may stop and restart, there may be a mix of continuous, discrete dynamics or spiking, thresholds are common, and the network topology may change in time (both connection and node structure).  There may also be local times – defined on nodes or connections – and adaptation and control play an important role. Networks may have function – getting from initial state A to final state B in finite time (usually impossible in if the model consists of analytic ODEs).

We describe our model for Asynchronous networks and the main objective: finding a coherent way to a apply a reductionist approach to complex heterogeneous networks. We also aim to give most of the proof of the factorization of dynamics theorem. Notes (with extensive references) will be provided.

Assessment:
MSci, MSc and PhD students can take this course for credit. Students taking the course for credit are to prepare an essay (counting for 60%) and give an oral presentation about their work (counting for 40%). If you are interested, please contact Prof Jeroen Lamb (jeroen.lamb@imperial.ac.uk) to make your interest known.