A 2D free boundary cell motility model with nonlinear diffusion yields an explicit curvature formula K2 that is claimed to determine whether the pitchfork bifurcation to traveling waves is direct or inverse.
Phase-field model of cell motility: Traveling waves and sharp interface limit
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Change of bifurcation type in 2D free boundary model of a moving cell with nonlinear diffusion
A 2D free boundary cell motility model with nonlinear diffusion yields an explicit curvature formula K2 that is claimed to determine whether the pitchfork bifurcation to traveling waves is direct or inverse.