  We study the semiclassical limit of the anisotropic two-photon Dicke model
with a dissipative bosonic field and describe its rich nonlinear dynamics.
Besides normal and 'superradiant'-like phases, the presence of localized fixed
points reflects the spectral collapse of the closed-system Hamiltonian. Through
Hopf bifurcations of superradiant and normal fixed points, limit cycles are
formed in certain regions of parameters. We also identify a pole-flip
transition induced by anisotropy and a region of chaotic dynamics, which
appears from a cascade of period-doubling bifurcations. In the chaotic region,
collision and fragmentation of symmetric attractors take place. Throughout the
phase diagram we find several examples of phase coexistence, leading to the
segmentation of phase space into distinct basins of attraction.
