isomorphic equations W. Ross Ashby states in his book "An Introduction to Cybernetics" that the system:
$\ x' =  1/2(x^2+y^2) + x*y + y$
$\ y' =  1/2(x^2+y^2) + x*y + x$
is isomorphic to the system:
$\ u' =  -u$
$\ v' =  v + v^2$
under the transformation:
$\ u =  x - y$
$\ v =  x + y$
can someone explain this properly?

Note that you can express $x$ and $y$ in terms of $u$ and $v$:
$$x=\frac{u+v}2\\y=\frac{-u+v}2$$
So, from the first equation of your system,
$$x' =  \frac12(x^2+y^2) + xy + y,$$
we have
$$\left(\frac{u+v}2\right)' = \frac12\left(\left(\frac{u+v}2\right)^2+\left(\frac{-u+v}2\right)^2\right) + \left(\frac{u+v}2\right)\left(\frac{-u+v}2\right) + \left(\frac{-u+v}2\right)\\
\frac{u'+v'}2 = \frac12\left(\frac{u^2+v^2}{2}\right) + \frac{-u^2+v^2}4\ + \frac{-u+v}2\\
\frac{u'+v'}2 = \frac{-u+v+v^2}2$$
$$
u'+v' = -u+v+v^2\tag{$*$}
$$
So that simplified nicely. Now do the same with the second equation, put the result together with $(*)$, and see what happens.
