The existence of the bifurcation implies that the kind of race an incumbent may face can vary greatly in response to relatively small changes in circumstances. A small change in the challenger's quality or in the type of service going to the district can change the race qualitatively, from one in which the incumbent has a stable advantage to one in which not only the incumbent's chances of winning and the amount of money dumped into the campaign but also the commitments the candidates make regarding post-election service may undergo substantial, growing oscillations.
Even when the incumbent's advantage is dynamically stable, the path of the campaign is a spiral. The incumbent's expected share of the votes, both the incumbent's and the challenger's financial support, the candidates' respective service commitments and much else will all inevitably oscillate during the campaign. These oscillations are not random wobbles, but rather reflect mutual, multiway strategic adjustments chosen by many of those who are interested in the election outcome. In many cases the variations will not be large enough to make a substantive difference, but a candidate or contributor observing a change of direction as it is occurring cannot be confident that the flow of the campaign is not about to wander dramatically from whatever the current situation may be. Usually the incumbent will win, but every incumbent has reason to be nervous.
The bifurcation pattern of oscillations and qualitative sensitivity to small changes will tend to dominate other patterns that may reflect alternative strategies, additional participants or other deviations from the specification of the current formal model. The theorems from local bifurcation theory that prove the robustness of the normal form equations (2) imply that, near the dynamic equilibrium point, motion in accord with the qualitative features that the equations describe will tend to be orders of magnitude larger than other features of the flow of the campaign.