Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 33A / c / Solution

For $\mu \gg 1$, trajectories rapidly approach the cubic nullclineand then move slowly along its attracting outer branches $|x|>1$. For $0<F<1$, the equilibrium lies on the repelling middle branch. Slow motion to a fold, a rapid jump to the opposite outer branch, and repetition produce a relaxation oscillation. For $F>1$, the equilibrium lies on the attracting right branch; trajectories undergo any necessary fast jump and then drift to that equilibrium, so no relaxation cycle remains.