Research interests
Of general interest
Lectures by Michael Thompson on Nonlinear Dynamics can be found on www.youtube.com/user/MichaelThompsonChaos/videos.
Climate tipping (papers)
- Theme Issue of Philosophical Transactions of the Royal Society Series A on Influence of Nonlinearity and Randomness in Climate Prediction, (Link to Preprint collection)
- Talks: Newton Institute (video, Cambridge 2010, go one level up for more talks), ICIAM (slides only, Vancouver 2011),
Continuation for experiments (papers)
- Introductory Physical Review Focus article by Mike Wofsey covering the first test on real pendulum experiment (also featuring small videos).
- Supported by EPSRC Grant EP/J010820/1 Control-based bifurcation analysis for experiments (2012-2014), EPSRC Fellowship EP/N023544/1 Exploring instability in complex systems - simulations in no-man's land (2017-2021),
EPSRC grant EP/V04687X/1 Developing strategies to prevent collapse of the Amazon rainforest (2021-2022) with Researcher Co-investigator Bert Wuyts - The basic mathematics behind it explained for a simple mechanical experiment (with animation but only based on numerical simulations).
- The method has been used in more advanced experiments with energy harvesting mechanical oscillators and wind tunnel wing tips by David Barton, on beams by Ludovic Renson, and on pedestrian crowd experiments and simulations by Jens Starke.
- A poster explaining a simplified version of the approach for steady states (also applicable in a statistical mechanics sense) is on Figshare.
Delay-differential equations (papers)
- Introductory poster (pdf) on delay effects in balancing
- Current maintainer of DDE-BIFTOOL, a numerical continuation software for delay-differential equations. Links:
- Download stable version: sourceforge.net/projects/ddebiftool, development version: sourceforge.net/p/ddebiftool/git/ci/master/tree (then use git clone, as instructed or download snapshot)
- Documentation: http://ddebiftool.sourceforge.net.
- Original website at KU Leuven keeping versions up to 3.0: http://twr.cs.kuleuven.be/research/software/delay/ddebiftool.shtml
- Colleagues: Prof. Bernd Krauskopf
- Collaboration (I am Associate Investigator) in project Feedback loops in climate systems: the maths of delays and the consequences (PI: Bernd Krauskopf, other AIs: AR Humphries, Henk Dijkstra) on Marsden Fund grant, 2020-2023
Bifurcations of smooth and piecewise smooth systems (papers)
- Material from Advanced Summer School on Continuation Methods for Nonlinear Problems, University at Illinois, Urbana Champaign 2018: lecture notes, supporting material
- Numerical continuation software COCO tools for continuation (by Harry Dankowicz, Frank Schilder)
- Colleagues and projects: Filippov system solver (by Petri Piiroinen)
- General purpose: efficient scripting interface for AUTO: RAUTO (by Frank Schilder)
- Material from LDSG Graduate School 05/06: lecture slides, supporting material
Nonlinear dynamics in semiconductor lasers (papers)
Subject of my PhD thesis, see webpage for the research group Laser dynamics at the WIAS.
Others
- Numerics of differential-algebraic equations (subject of my master thesis)