Re: Can Matlab even do this?

In article <ef2d4b6.1@xxxxxxxxxxxxxxxx>, "Tim Felty"
<felty@xxxxxxxxxxxxxx> wrote:

Actually I need to find if there are any coefficients A, B, C, and D
that satisfy that relationship.

The idea is that there is a system with feedback. The forward system
is an arbitrary function, and the feedback system is probably linear,
but not necessarily. From these I determined the criterion for there
to be points at which the output of the forward system oscillated
between.

So if the forward function is f(x) and the feedback system is g(x)the
necessary relationship to be satisfied is
x1=g(f(g(f(x1)))). What I had above is for the case of
f(x)=a*x1+b and g(x)=x/c. The second one was for
f(x)=A*exp(B*x)+C and g(x)=x/D.

So I'm trying to find a way to either show that no possible values
for A, B, C, or anything else for any value x1, or if there are
values that satisfy these relationships for ranges of x1, what they
are, and how to find them.

I hope this helps clarify things.

Thanks
Tim Felty
-----------------
I think my question is still unanswered. It is this. In your equation

x1=g(f(g(f(x1)))) ... (1)

do you want this equality to hold for all possible values of x1 or for a
select few, perhaps one? If it is to hold for all x1, that is what I
referred to as an "identity".

In the case, f(x)=a*x1+b and g(x)=x/c, there are certainly values of a,
b, and c that would make (1) an identity, but they are not unique. All
you need is to have either a = c and b = 0, or a = -c, and this allows
infinitely many possibilities.

In the case, f(x)=A*exp(B*x)+C and g(x)=x/D, it is not hard to prove
that no possible combination of values A, B, C, and D could ever make (1)
an identity. Just consider what happens to the two sides of
x1=g(f(g(f(x1)))) as you allow B*x1 to approach plus infinity. The right
side will approach either +infinity or else the constant C/D, depending on
the sign of A/D. If it's a constant, that is certainly incompatible with
the left side. If it's an infinity, its doubly exponential nature will
eventually outrun the linear x1. Hence, no values for A, B, C, or D can
ever make (1) an identity.

(Remove "xyzzy" and ".invalid" to send me email.)
Roger Stafford
.

Relevant Pages

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