River deltas are under external stress from sea-level rise, subsidence, and decreases in sediment and water discharges caused by anthropogenic activity. Naturally, delta channels respond to these stressors by avulsing and bifurcating. Avulsion involves an abrupt change of channel course that changes the locus of sediment deposition. Bifurcation occurs in the most seaward parts of river deltas where channels divide due to mouth bar deposition. However, how avulsion (top-down) and bifurcation (bottom-up) processes interact in river deltas is poorly understood. We conducted a suite of morphodynamic numerical model experiments using six scenarios with different slopes, selected within the range observed in natural deltas, upstream from the delta apex. The experiments allow us to understand the internal (autogenic) interaction of avulsion and bifurcation in the absence of external (allogenic) forcing. We find that topset slope (S_topset) primarily controls the avulsion timescale (T_a) with T_a = 0.3S_topset^-1.18 (R² = 69%; p < 0.05). Avulsion and bifurcation are shown to occur simultaneously based on the non-unimodal distribution of dimensionless island sizes created in our model, even though these are mechanistically different processes. Comparing our findings to natural deltas, we find consistent avulsion timescale-topset slope (T_a-S_topset) relationships. Our findings show how the delta topset slope serves as the first order control of the avulsion timescale, and how avulsion and bifurcation interact throughout delta building processes. This interaction is significant due to their direct impact on coastal and inland hazards that arise from rapid geomorphic change and flooding on densely populated deltas.