Representation formulas for stationary solutions of a cell polarization model

Abstract

We are interested in the global bifurcation structure of solutions for a nonlinear boundary value problem with nonlocal constraint (SLP) that appears in a cell polarization model with mass conservation proposed by Y. Mori, A. Jilkine and L. Edelstein-Keshet. We obtained primitive representation formulas of all solutions and investigated a surface \({\mathcal {S}}\) consisting of all bifurcation diagrams with heights. However, we could not find any parameterization of the surface \({\mathcal {S}}\). In this paper, we show parameterizations of the surface \({\mathcal {S}}\) and concrete representation formulas of all global bifurcation diagrams of (SLP). These results are also beneficial for numerical computations to get all bifurcation diagrams. We propose new methods in view of them.