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.
Traveling Motility of Actin Lamellar Fragments Under spontaneous symmetry breaking
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abstract
Cell motility is connected to the spontaneous symmetry breaking of a circular shape. In https://doi.org/10.1103/PhysRevLett.110.078102, Blanch-Mercader and Casademunt perfomed a nonlinear analysis of the minimal model proposed by Callan and Jones https://doi.org/10.1103/PhysRevLett.100.258106 and numerically conjectured the existence of traveling solutions once that symmetry is broken. In this work, we prove analytically that conjecture by means of nonlinear bifurcation techniques.
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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.