= Pitchfork reversal near geometric ratio two in magnetoconvection
{title2=$\varphi_c=2+\zeta^2(1+q)/q+O(\zeta^4)$}
Put $m=(4-\varphi)\zeta^2/\varphi$. The derivative of the <stationary branch of five-mode magnetoconvection> at $a^2=0$ is $r_2=1+q+q(2-\varphi)/m$. For fixed positive $q$ and small $\zeta$, it changes from a forward to a backward <pitchfork bifurcation> direction at the displayed value. Expanding the exact numerator $q\varphi(2-\varphi)+(4-\varphi)\zeta^2(1+q)$ gives this result. The expansion in amplitude requires $a^2\ll m$; branch direction alone does not determine stability against all other modes.
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