Why politics makes strange bedfellows: Dynamic model with DNS curves

We analyze a two-dimensional system of political behavior which has three e quilibria in the uncontrolled version. After adding a control variable, two more equilibria occur and Skiba curves (also called DNS curves) can be ana lyzed. In this model, it is possible to derive under what conditions each o f the different equilibria is a saddle point, a node, or a focus. In partic ular, for certain parameter ranges, all five equilibria have real eigenvalu es. In this case, the Skiba curves can be computed in a more straightforwar d way than usual. The curves spiral outward, so any ray extending from the origin crosses these curves arbitrarily many times, as it alternately cross es regions for which it is optimal to approach each of the three equilibria .