I have a system of ODEs with parameters, p[i], and variables, x[i].
f := [
associated with the innitial conditions:
[x(0) = p, x(0) = p].
I am interested in sets of parameters where the solution x(t) is the same; if [p,p,p] is associated with a solution x(p,t), and [ph,ph,ph] is asociated with the solution x(ph,t); then x(p,t)=x(ph,t) for all t if and only if
[ph = ph,
ph = p,
ph = -p*p^2+p^2*ph+p]
i.e. ph takes any real value, ph takes the same values as p and ph takes a value determined by the original parameter vector and ph.
In a previous question it was demonstrated that x(ph,t)/x(p,t) rapidly converge on p as t increases for a specific parameter vector that was given in the question (see graph below)
This raises the question does this limit generally hold?
I have struggled to do this in maple and I am suspicious of the answer i have got
limit (x(ph,t)/x(p,t),t=infinity)=+/- infinity
My question is
+ when does a finite limit exist?
+ what is the finite limit?