Let's consider a network of interacting dynamical systems comprising 2 populations (A and B) where the mean field description of the dynamics of the 2 populations is captured by the following equations:
\begin{align} \frac{dx_A}{dt} &= - x_A + p_{AA} J_{AA} x_A - p_{AB} J_{AB} x_B + g_A\\ \frac{dx_B}{dt} &= - x_B + p_{BA} J_{BA} x_A - p_{BB} J_{BB} x_B + g_B, \end{align}
where the variables $p_{ij}$ follow each their own ODE dynamics, that depend on some parameter $\alpha$ (the exact form of the equations is not relevant for the question).
It turns out, that by changing the value of $\alpha$, of course the dynamics of $x_A$ and $x_B$ change, but not in a qualitative manner to indicate a phase transition.
However what changes qualitatively by changing $\alpha$, is the response of $x_A$ to external perturbations. In fact one can define a critical $\alpha_C$ as a transition point, where the response of the system (and in particular $x_A$) is qualitatively different when $\alpha<\alpha_C$ and $\alpha>\alpha_C$.
Can one say that we have a phase transition here?
(The stability of the system doesn't change)
Are you aware of a similar phenomenon on any known system? Or do you have any relevant literature to recommend for further reading on the topic?