Fig. 4.

Tipping points in the effects of an exogenous shock. In all three panels, $\alpha$ = $\beta$ = 0.5. A shows a clockwise hysteresis loop traversed by the system with the increasing strength of an external shock, about which all agents initially agree. B and C illustrate bifurcation in the polarization trajectories for shocks that occur within the critical region depicted in A ($\gamma$ = 0.45). The black lines show the trajectories of the 10 preexisting issues (excluding the shock), and orange shows the trajectories of disagreement regarding the shock. The shock occurs at a level of polarization ($\sigma$ = 0.65) at which the probability to polarize reaches 0.5. B shows how a shock can reverse a polarizing trajectory, while C shows how the recovery can also fail, even though all parameters are identical to those in B. See SI Appendix, Fig. S9 for the effects of an exogenous shock on partisan difference.