[en] Particle tracking simulation studies of the beam-beam interaction (BBI) in circular colliders require large amounts of CPU time to determine particle distributions out to large amplitudes. This is due to the limited number of superparticles simulated and the rarity of correlated events which can drive a particle to such amplitudes. An alternative approach for determining the final particle distribution out to large amplitudes is explored. The method employs a combination of particle tracking over selected regions of the amplitude space followed by the solution for the equilibrium distribution of the particle flow through this space. The technique is described and preliminary results, when applied to the two-dimensional case are given