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In article <Pine.OSF.3.91.970904103245.24984B-100000@leofric>,
Ian Clarkson  <csx181@coventry.ac.uk> wrote:
>
>
>Hi everyone,
> In the world of System and Control Theory there are such things as 
>"Neutral Systems" and what I was hoping was that someone may be able to 
>tell me where the name neutral comes from.
>
>A Neutral system is a system of the form (in state-space form)
>
>x'(t) = f(t,x'(t-h))
>
>where x(t) is the state and h is a constant dely.
>
>I have looked at numerous early references on this area but find no 
>mention of the origin of the name "Neutral". 
>
>Is there anyone who can enlighten me?
>Thanks in advance.
>Regards.
>Ian.
>---
>Ian Clarkson,
>Control Theory and Applications Centre,     
>Coventry University.                       
>
It's not a misspelling of "neural systems," in this case.
Neither is the quoted example neutral...  x'(t) = f(t,x'(t-h)) is a 
functional differential equation of retarded type (= retarded system);
 x'(t) = f(t, x'(t+h)) is of advanced type.
  x'(t) = f(t, x(t+h), x'(t-h)) is said to be of neutral  type-- it has
properties of both the others (to anser Ian's question).
 Jack Hale has studied these -- see  his
work on functional differential equations.

David E.

-- 
 David L. Elliott, Vis. Sr. Research Scientist, Inst. for Systems Research,
 University of Maryland, College Park, MD     | delliott@ISR.umd.edu   
 "A pig cannot write if he                    | http://www.isr.umd.edu/~delliott
  has no oink in his pen."  --Col. Lemuel Q. Stuelpnagel