E> UK NONLINEAR NEWS (November 1997): Editorial UK Nonlinear News , November 1997.

Editorial: Nonlinear Dynamics - A State of Mind

John Brindley

The recent conclusion of the UK EPSRC Applied Nonlinear Maths programme prompted a few memories. Almost exactly 13 years ago a group of us at Leeds formed the first Executive Committee of a Centre for Nonlinear Studies. The composition of the group, David Crighton (Maths), Peter Gray ( Chemistry), Alan Wilson ( Geography), Chris Taylor (Engineering), Arun Holden (Physiology), Philip Gaskell (Fuel & Energy) and myself (Maths) hints at the range of interests spanned by the Centre, and, though (a few) other Centres had preceded it in foundation, such a range was unusual if not unique at that time. Shortly afterwards, the UK SERC initiated a special programme in Nonlinear Systems (NLS), which was to run for 5 years and provide life blood support both for the development of dynamical systems methodology and for the training of a cohort of young scientists. Anxious to exploit their toolkit wherever opportunity beckoned, some of this cohort, and some of mellower vintage, were (relatively) generously supported in the UK by the Applied Nonlinear Mathematics (ANM) initiative of SERC, later transmuted to EPSRC. The range of projects supported by ANM, (which I will not attempt to summarise, just look at the recent "Research Highlights" glossy), far transcends the span of that early Leeds CNLS group, penetrating the furthest corners of the biological, physical and engineering sciences, and pushing open the doors of medical science, though perhaps disappointingly failing to engage yet with the fuzzy problems of human and social sciences.

So, after this long protected childhood, do we have a rounded adult product able to take a respected place in the world? The answer must be yes, not so much in the form of a recognisable body of finite size, called nonlinear something or other, but more in an all pervading attitude. When, many years ago as Director of the Leeds CNLS, I was asked what it was, I often replied, "a state of mind". That state of mind has proved infectious, and broadened our approach to mathematical modelling of many ever more complex phenomena. I am confident that the readers of this article will ensure that the momentum is not lost, either in new mathematical development or in novel application; the world is yours to conquer.

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