Impact of meridional flow variations on solar cycle asymmetry. Panel (a): results when the meridional flow is modulated according to the active region eruption belt (butterfly diagram). The modulation was applied using the term δvsin²(2θ_max), where θ_max is the most probable eruption latitude – corresponding to the location of the strongest toroidal field. The black curve (right y-axis) shows the magnetic energy density evolution, while the blue curve (left y-axis) shows the amplitude variation of the meridional flow. Panels (b)–(e): asymmetry measures derived from the same simulation. These four panels represent the same quantities as in Fig. 3. We also include an additional 50% stochastic fluctuation in the poloidal field generation mechanism. In this scenario, the meridional flow speed weakens near the solar cycle maximum.