Invisible wrote:
> Consider a point exactly between two attractors. A particle at this 
> point experiences zero resultant force. Purturbing the point by any 
> finite amount to either side will make the resultant force non-zero. 
> This will cause a different path to be traced, regardless of how much 
> damping is applied.
> 
> In general, applying more damping makes the system *less* unstable, but 
> does not remove areas of chaotic behavious; it just makes them smaller.

I think you may have some misconceptions about what chaos is.  First 
off, sensitivity to initial conditions is a necessary but *not 
sufficient* condition for chaotic behavior.  Secondly your example of a 
point between the two attractors only argues for this sensitivity at a 
manifold of points, and many many non-chaotic systems have such a 
feature (for example a simple pendulum).

Thirdly, although it's possible I'm wrong here, if you have *any* 
dampening I don't think the system can be counted as chaotic because all 
paths will eventually converge to a point.  If the system would be 
chaotic without dampening it's sort of a minor point since it can still 
look a lot like chaos, but technically I think it's incorrect to call it 
chaotic.

Finally, I'm not sure that your system is chaotic.  For inverse-square 
springs it's known as Euler's three-body problem and appears to have a 
(rather complicated) analytic solution.

Post a reply to this message