Existence, Uniqueness & Bifurcations · Superchallenge problem

The state of a system obeys $y' = h + y - y^3$, and the parameter $h$ is swept very slowly: up from a large negative value to a large positive value and back. The state tracks a stable equilibrium until that equilibrium disappears in a saddle-node bifurcation, then jumps straight (at constant $h$) to the other stable branch. In the $(h, y)$-plane the path traces a closed hysteresis loop. Find the area enclosed by the loop.