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.