I found the following set of autonomous nonlinear ODE's in recent
work on self-exciting dynamos:
where a,b,k, and l are real and positive constants and f(x)=(1-e+ex), where e ranges from 0 to 1.
There is evidence (from bifurcation analysis and calculations made using an electronic circuit as an analogue computer) that the `volume' of the regime of nonsteady (including chaotic) solutions in (a,b,k,l) parameter space decreases with increasing e and vanishes altogether in what is possibly the geophysically and astrophysically most interesting case, namely when e=1. Some progress has now been made towards a physical interpretation of this `nonlinear quenching' phenomenon.
I wonder whether these equations have been studied in other contexts?
UK Dynamics Days (28 June - 1 July 1998, Edinburgh) planning is well underway. For more information see: http://www.fen.bris.ac.uk/engmaths/research/nonlinear/ddays.html .
Our web site is now up ( http://chaos-mac.nrl.navy.mil/) although still under some construction -- and maybe not really ready for prime time. We invite visitors. If you have a nonlinear dynamics or related Web site, please add a link to ours. Also, please tell us your address so we can set links to it.
We have available in PDF or HTML format several of our recent papers. If you cannot read these formats, let us know and we will send you hard copy.
A new textbook on Fractals and Chaos has recently been published.
Fractals and Chaos: An Illustrated Course.
Paul S Addison.
Institute of Physics Publishing, Bristol, 1997.
This is very general in nature and is aimed at 2nd/3rd year Engineering and Science undergraduates. It is also potentially useful for postgraduates who want a quick introductory overview of the twin subjects. More information is available at http://www.napier.ac.uk/depts/cte/staff/paddison/book.html.
Version 2.2 of the free C++ software package `doubledouble' has been released. `doubledouble' implements doubled-double (at least 30 decimal place) floating point arithmetic on IEEE 754 floating-point hardware.
This code was developed for simulation studies of dynamical systems, for cases where double precision is insufficient.
This is the probably the simplest way to increase the precision of existing double-precision C or C++ code. For many programs, all that is required to convert to doubledouble is the addition of two lines:
#define double doubledouble
The code may be downloaded from http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html.
Deadlines are 1 February 1998 for poster contributions and 1 March 1998 for registration.
For further details see the website at http://www.bath.ac.uk/Departments/Biosciweb/mathconf.htm or contact Nick Britton at firstname.lastname@example.org.