Bifurcation diagram of the 2023 Cambridge quadratic-product system
= Bifurcation diagram of the 2023 Cambridge quadratic-product system
The equilibria of $\dot x=(a^2-x)(a-y^2)$, $\dot y=x-y$ lie on
$$
x=y=a^2
$$
for every $a$, and on $x=y=\pm\sqrt a$ for $a\geq0$. They meet in a <subcritical pitchfork bifurcation> at $a=0$; the positive square-root branch meets the $a^2$ branch and exchanges stability in a <transcritical bifurcation> at $a=1$.