Codimension-two bifurcations in single-mode optical bistable systems

The codimension-two bifurcation set of single-mode optical bistable systems is investigated. The entire set is classified into three classes, a cusp bifurcation set, a degenerate Hopf bifurcation set, and the intersection of a Hopf bifurcation and a saddle-node bifurcation. Based on the specification of degenerate Hopf bifurcation, super- and subcritical Hopf bifurcations can be identified. It is found that, in the subcritical Hopf bifurcation region, an attractor of time-dependent motion may coexist with the stable stationary solution when the cavity is filled by a passive medium. Moreover, the coexistence of three attractors is observed for certain parameter combinations.