In this talk, we deal with the Gierer-Meinhardt reaction-diffusion model with advection term on the $Y$-shaped metric graph. The $Y$-shaped metric graph is a domain consisting of three finite segments joined a single junction. Moreover, we consider the advection velocity changes from segment to segment. We present the result on the existence of one-peak stationary solutions for the Neumann boundary condition and the Robin boundary condition, respectively. In particular, the location of a spike is decided by the three effects, the network structure of the $Y$-shaped graph, the choice of the boundary conditions, and the sign of the advection velocity.