Disclaimer. I'm not a physicist.
Consider a physical system whose "energy" $E$ is a function of $k$ real parameters $\theta = (\theta_1,\ldots,\theta_k) \in \mathbb R^k$. Let $E_{\min}$ be the minimum possible energy for the system (e.g zero). Let $c \in \mathbb R$ be a fixed scalar (say, $0$, $\pi$, $e$, etc.)
Question. In physics, is there a standard terminology for the scenario where $E(\theta) = E_{\min}$ whenever $\theta_1 = c$ (irrespective of the other $k-1$ parameters of the system) , while $E(\theta) > E_\min$ otherwise. That is, every configuration $\theta$ has minimal energy if and only if the first parameter $\theta_1$ is fixed to the value $c$.
For example, could one say something like "A global bifurcation of co-dimension 1 occurs at $\theta_1 = c$. " ?
