Codimension-two two-hard-mode bifurcation and coexistence of multiple attractors in a two-photon laser with an injected signal.

Abstract

A codimension-two Hopf bifurcation and the coexistence of multiple attractors of a two-photon laser with an injected signal are investigated. The quasiperiodic motion with two incommensurate frequencies (2-torus) may arise directly from a stationary solution through the type-III codimension-two bifurcation mechanism. We analyze conditions and identify the quasiperiodic motion in terms of time-dependent solutions and Poincar\'e maps. Moreover, the coexistence of multiple attractors in the vicinity of the type-III bifurcation point and the symmetry-breaking bifurcation can be observed as well.