## Solution The diagram shown is a classic **bifurcation diagram** for a **saddle-node bifurcation** (also called a fold bifurcation). The characteristic "parabolic" shape, with two fixed points merging and annihilating each other as the parameter is varied, is typical. ### Standard Form The standard differential equation exhibiting this bifurcation is: \[ \frac{dy}{dt} = a - y^2 \] - Here, \( a \) is the parameter. - For \( a > \), there are two fixed points (\( y = \pm\sqrt{a} \)). - For \( a = \), there is one fixed point at \( y = \) (double root). - For \( a < \), there are no real fixed points. ### **Answer** \[ \boxed{ \frac{dy}{dt} = a - y^2 } \] This is the differential equation corresponding to the bifurcation diagram shown.