(a) Effect of varying N_ρ (in red, Ra/Ra_cr = 32) and Ra (in blue, N_ρ = 6) on the local Rossby number calculated based on the convective length scale l_conv (3). Dotted line denotes Ro_l = 1, e.g., a balance between inertia and the Coriolis force. (b) Density contrasts N_ρ and Rayleigh numbers $\stackrel{\sim }{\mathit{Ra}}$ spanned by simulations in this work. Different symbols denote three dynamical regimes of the flow, discussed in more details in Sect. 3. Filled (empty) triangles, predominantly multipolar fields with solar (anti-solar) differential rotation (Sect. 3.2). Circles, quadrupolar oscillatory dynamos with solar-like differential rotation (Sect. 3.3). Diamonds, reversing dipole-multipole solutions with transitions between three-layered and anti-solar rotation (Sect. 3.4). Solar- and anti-solar differential rotation is shown in the inset plots depicting zonal flows ⟨u_ϕ⟩_ϕ for N_ρ = 2, $\stackrel{\sim }{\mathit{Ra}}=32$ (left) and $\stackrel{\sim }{\mathit{Ra}}=96$ (right).