Dynamics of curved fronts in systems with power-law memory

A simple model of Keratocyte membrane dynamics: The case of motionless living cell

“…Thus, the result of [14], obtained with diffusion terms neglected, is recovered from our more rigorous and precise equation (25). However for other values of parameters and when the initial curvature is large in some points the simulations of equations (25), (30) revel a significant deference see Fig Plots of the function f (R) in (17) for the values β = 1, 0.5 that manifest stable and unstable states, and for the value β = 0.3 that is nonphysical since it does not include any steady states. We use the same values of parameters as in…”

“…We have performed an analysis of the cell surface dynamics in the framework of the minimal phase field model of cell motility that was developed and investigated numerically in [1], [13], and [8], where the order parameter u is coupled with polarization (orientation) vector field P of the actin network. We considered the axisymmetric case (circular shape interface), where we obtained a closed ordinary differential equation describing the evolution of the radius (17). We found the minimum value β c for the actin creation that is compatible with the existence of a stationary cell solution (18).…”

“…For the first integral (22) we refer the reader to [17] where we calculate the same expression in details. For the integrals (23), (24), notice that the terms dependent on (θ, t) are vanish.…”

“…For investigating the stability of the circular stationary frontR(t) that is governed by (17) we substitute the disturbance,…”