MadSci Network: Physics
Query:

Re: Is there any way to calculate the inflex point of a non linear system.

Date: Tue Jan 27 15:33:16 2004
Posted By: Guy Beadie, Staff, Optical sciences, Naval Research Lab
Area of science: Physics
ID: 1074717926.Ph
Message:

Hello, Ryan.

Youíve asked a good, but very difficult question.  Unfortunately, I donít 
think I can answer it directly.  The inflex point, or point of inflection 
of a dynamical system has some general properties, but if you need help 
finding such a point youíll have to include more information about the 
system youíre looking at: the way youíd find one depends entirely on the 
specifics of your system.

It is possible, though, that you could find your inflection point if you 
had a better handle on the definition, or if you saw some examples of 
inflection points in other systems.

I found a great resource on nonlinear systems, The World of Bifurcation, 
while searching for information:
 http://www.bifurcation.de/

This site contains several very informative tutorials, in addition to 
example dynamical systems which exhibit bifurcations.  The tutorials cover 
not only the types of bifurcation phenomena (some of which arise from 
inflection points) but also how one traces the equilibrium curves of the 
system to find them.

Another resource is to scan the sci.Nonlinear FAQ:
 http://amath.colorado
.edu/faculty/jdm/faq.html

It has a section on bifurcation, along with some further links.

A less-useful but more-general resource is the following compendium of 
links to nonlinear dynamics sites:
 http://ar
chives.math.utk.edu/topics/nonlinearDynamics.html


Good luck, and Iím sorry I couldnít be more helpful,

  - Guy


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