The two-attracting-equilibria conjecture for the glacial cycles model

Let

$$\mathcal B=\left\{(w,\eta,\xi)\in\mathbb R\times[0,1]\times[0,1]\right\}.$$

For the piecewise-defined system, call an equilibrium regular if it lies in its associated domain, boundary if it lies on the boundary between domains and is an equilibrium of the adjacent vector fields, and virtual if it is an equilibrium of a vector field but lies outside that vector field's domain. Two-attracting-equilibria conjecture. Varying the ablation parameters $b_1$ and $b_2$ while fixing all other parameters, the system has two attracting equilibria on $\mathcal B$, and each equilibrium can be regular, boundary, or virtual. The conjecture is supported only by numerical simulations in the supplied text; no general proof or resolution is given.