It feels like a stupid question...
given the system:
$\displaystyle \frac{dx}{dt} = y$
$\displaystyle \frac{dy}{dt} = Ay-x(1-x)$
with x=x(t), y=y(t)
How would I rewrite the system in, say $\displaystyle \hat{t}=-t$?
I don't see how we could just make that step...
$\displaystyle \frac{dy}{d\hat{t}}=-\frac{dy}{dt},\frac{dx}{d\hat{t}}=-\frac{dx}{dt} $
Gives...
$\displaystyle -\frac{dx}{d\hat{t}} = y(t) $
$\displaystyle -\frac{dy}{d\hat{t}}= Ay(t)-x(t)(1-x(t)) $
I don't see how we could just subtitute $\displaystyle t= \hat{t}$ in the eqations...
A pity, or we could invoke this.No, they do not specifically represent anything...
I don't have any other answer, I'm afraid, other than I think you can just do it. I don't have a justification. This is the physicist part of me talking, I freely admit.