Abstract
A theory of the nonlinear dynamics of a biological double membrane with nonequilibrium chemical fluxes across both membranes is presented. A phenomenological free-energy functional is formulated that couples the intermembrane distance and the concentration between the membranes, as well as the dependence of the chemical fluxes on the intermembrane distance and membrane curvature. The derived nonlinear evolution equations for the double membrane dynamics are studied analytically and numerically. The linear stability analysis is performed and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane numerical simulations are performed that reveal oscillations in the chemical concentration and membrane shape.
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