In this paper a two-cell model, with hydrodynamic and sediment transport functions, has been used to simulate the progression of tidal estuary entrances to a quasi-equilibrium state. This state is an attractor, as used in the terminology of system dynamics. Prior experimental research suggested at least one, possibly two, attractors exist for this system. Two attractors were found; the hydrodynamics of entrances described by one attractor were tidally dominant, whereas those of the other attractor were dominated by river flow. Perturbations to the entrance state, such as those caused by floods, could result in an entrance moving from one attractor to another.