Fundamental and vortex dissipative quadratic solitons supported by spatially localized gain

We consider settings providing the existence of stable two-dimensional (2D) dissipative solitons with zero and nonzero vorticity in optical media quadratic ($\chi^{(2)}$) nonlinearity. To compensate spatially uniform loss both fundamental-frequency (FF) second-harmonic (SH) components system, a strongly localized amplifying region ("hot spot",HS), carrying linear gain, is included, acting onto either FF component or SH one. In cases, Gaussian radial gain profile supports fundamental pinned to HS. The structure stability domains for 2D rather complex. They demonstrate noteworthy features, such as bistability spontaneous symmetry breaking. A ring-shaped vortex solitons, winding number up 5, multipoles. Nontrivial transformation vortex-soliton profiles upon growth value stretching observed.