In article ,
"Bob Hobden" writes:
|
| Be kind to him. Elementary numerical analysis[*] isn't obvious to
| the uninitiated layman :-)
|
| [*] What are now often referred to as chaotic systems were referred
| to as numerically unstable ones when they were studied before about
| 1980. The problem is the same - the approach differs. I am no
| expert, but anyone insane enough to ask for a more detailed
| explanation is welcome to do so :-)
|
| Quite a good description of "chaotic systems" for the layman on...
| http://dept.physics.upenn.edu/course...tion3_2_5.html

Er, no. It's ghastly.

What scientists and mathematicians mean by chaos is very much
related to the spirit of the definitions given above. We state
that systems are chaotic if they:

1. are deterministic through description by mathematical rules.
2. have mathematical descriptions which are nonlinear in some way.

. . .

The surefire way to have a system described by an algorithm that
exhibits chaotic behavior is to have it be nonlinear.

This is absolute nonsense. It is possible to have linear systems
that are chaotic (though you have to get fairly abstruse, but it
is easy to have non-linear systems that are not chaotic. For
example:

x'' = -x^3

Ask me for a more accurate explanation, of you feel up to it, but
be warned that even a simplication gets recondite fairly fast.


Regards,
Nick Maclaren.