# Identifying the Differential Equation from the Bifurcation Diagram The diagram shown in your image is a classical **saddle-node (or fold) bifurcation**. This is indicated by the way two fixed points (one stable, one unstable) appear as the parameter \( a \) increases, and then disappear for lower values of \( a \). ## Standard Form The standard differential equation for a saddle-node bifurcation is: \[ \frac{dy}{dt} = a - y^2 \] - **\( a \)** is the bifurcation parameter. - For \( a < \), there are no real fixed points. - For \( a = \), a single (degenerate) fixed point at \( y = \). - For \( a > \), two fixed points at \( y = \pm\sqrt{a} \). ## Answer \[ \boxed{ \frac{dy}{dt} = a - y^2 } \] This equation matches the bifurcation diagram shown in your image.