I am a Professor of Applied Mathematics, having previously held chairs in UMIST and Queen Mary, University of London (the photo shows me discussing something vitally important with Jaroslav Stark who sadly died in 2010. I am co-editor of a special issue of Dynamical Systems an International Journal deedicated to his memory. You can find another photo of me on Nick Gilbert and Marc Atkins' Faces of Mathematics home page -- this forms part of an EPSRC project a few years ago.

If you are thinking of doing a Ph.D. with me then you should get an application form from our Postgraduate pages. It is also a good idea to email me so that we can talk about what you might do.

You can find more details of the people I work with and my academic career. Some of my papers (and a list of other papers) are also available. I also have some personal links. Recent papers can be downloaded from the departments eprint server.

Research Interests

I am interested in most areas of dynamical systems -- particularly bifurcation theory for maps and flows. I would welcome approaches from prospective Ph.D. students who are interested in working in this area. My current research is in four main areas:
• Bifurcation theory (particularly global bifurcations)

  My current work here focusses on bifurcations from trajectories of differential equations which extend to infinity (examples are the Falkner-Skan equations and the Nose equations). These are still very poorly understood except on an example by example basis. Much of this work is in collaboration with Sir Peter Swinnerton-Dyer at the Newton Institute in Cambridge.

• Synchronization and blowout bifurcations

  Identical, globally coupled systems can have synchronized states in which every system behaves identically. Bifurcation curves corresponding to bifurcations in which typical chaotic synchronized solutions become unstable may be extremely complicated (fractal). This is associated with blowout bifurcations from the synchronized state (the loss of transverse stability of atypical sychnronized states embedded in the chaotic attractor) in ways which are not completely understood.

• Low dimensional maps

  It may seem surprising, but there is still a fair amount we do not know about maps as simple as x goes to rx(1-x) with r>0.

• Quasi-periodically forced systems

  Computer simulations of the behaviour of quasi-periodically forced systems suggest that very wierd things can happen (strange non-chaotic attractors, for example). We have been trying to understand different features of these systems, both for maps (with groups in Germany, USA and London) and for flows. The picture shows an example -- as a parameter is changed by a small amount two stable curves collide with an unstable curve to create what appears to be a strange non-chaotic attractor. We don't know whether this is really what is going on, but it is interesting to speculate.

  
  
  If you want a list of recent papers, some of which you can read in pdf format, or download as tex files, click here.

Some past and present PhD students of mine are :

• Phil Ramsden (1998 - ...)
• Murad Banaji (1997 - 2001) Identically coupled oscillators
• Mark Johnston (1994-1997) Coupled map lattices
• Carlo Laing (1994-1997) Coupled oscillator networks
• James Robinson (1991-1994) Inertial Manifolds
• Toby Hall (1988-1991) Periodicity in chaos

Teaching

• (MATH20951) Financial Mathematics for Actuarial Science II (Semester 1)

  Course materials for this course are available through the Blackboard system.

• (MATH34042) Discrete Time Dynamical Systems (Semester 2)

  Course materials for this course are available through the central School pages and the university Blackboard system.

A bit more about me

I'm not sure how much more you want to know, there is more academic stuff here or you could try some personal links.

Last up-dated Feb 2012.