  A Bose-Einstein condensate in a double-well potential features stationary
solutions even for attractive contact interaction as long as the particle
number and therefore the interaction strength do not exceed a certain limit.
Introducing balanced gain and loss into such a system drastically changes the
bifurcation scenario at which these states are created. Instead of two tangent
bifurcations at which the symmetric and antisymmetric states emerge, one
tangent bifurcation between two formerly independent branches arises [D. Haag
et al., Phys. Rev. A 89, 023601 (2014)]. We study this transition in detail
using a bicomplex formulation of the time-dependent variational principle and
find that in fact there are three tangent bifurcations for very small gain-loss
contributions which coalesce in a cusp bifurcation.
