A main objective of topological photonics is the design of disorder-resilient optical devices. Many prospective applications would benefit from nonlinear effects, which not only are naturally present in real systems but also are needed for switching in computational processes, while the underlying particle interactions are a key ingredient for the manifestation of genuine quantum effects. A particularly attractive switching mechanism of dynamical systems are infinite-period bifurcations into limit cycles, as these set on with a finite amplitude. Here we describe how to realize this switching mechanism by combining attractive and repulsive particle interactions in a driven-dissipative Su-Schrieffer-Heeger model, such as realized in excitonic lasers and condensates so that the system displays a nonhermitian combination of parity and charge-conjugation (PC) symmetry. We show that this symmetry survives in the nonlinear case and induces infinite-period and limit-cycle bifurcations (distinct from a Hopf bifurcation) where the system switches from a symmetry-breaking stationary state into a symmetry-protected power-oscillating state of finite amplitude. These protected dynamical solutions display a number of characteristic features, among which are their finite amplitude at onset, their arbitrary long oscillation period close to threshold, and the symmetry of their frequency spectrum which provides a tuneable frequency comb. Phases with different transition scenarios are separated by exceptional points in the stability spectrum, involving nonhermitian degeneracies of symmetry-protected excitations.
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