  This work concerns the dynamics of conformal cubic scalar field on a
Schwarzschild--anti-de Sitter background. The main focus is on understanding
how it depends on the size of the black hole and the Robin boundary condition.
We identify a critical curve in the parameter space that separates regions with
distinct asymptotic behaviours. For defocusing nonlinearity, the global
attractor undergoes a pitchfork bifurcation, whereas for the focusing case, we
identify a region of the phase space where all solutions blow up in finite
time. In the course of this study we observe an interplay between black hole
geometry, boundary conditions, and the nonlinear dynamics of scalar fields in
asymptotically anti-de Sitter spacetime.
