Schematic plot of the neutral stability curves for pitchfork and Hopf bifurcation for double-diffusive convection showing the critical Rayleigh number as a function of wavenumber |$k$|⁠. The pink solid line refers to the loci of pitchfork bifurcation. The red circle markers identify locations where the Hopf bifurcation is the primary bifurcation. On the red dashed line without circle markers, the amplitude equations has two real eigenvalues that add up to zero. (⁠|$a$|⁠) |$Rs< Rs_c$| where pitchfork bifurcations are the primary bifurcation, (⁠|$b$|⁠) |$Rs= Rs_c$| where the pitchfork and Hopf bifurcation thresholds meet at a TB point and (⁠|$c$|⁠) |$Rs> Rs_c$| where the pitchfork and Hopf bifurcation can be primary bifurcations. In this case two TB points can be identified. The minima of the curves define the critical wavenumber and Rayleigh number. In the double-diffusion case, the wavenumbers are the same for both the pitchfork and Hopf bifurcations in (⁠|$c$|⁠).