Representation formulas for stationary solutions of a cell polarization model

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 form...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2022-12, Vol.39 (3), p.1025-1053
Main Authors: Mori, Tatsuki, Tsujikawa, Tohru, Yotsutani, Shoji
Format: Article
Language:English
Subjects:
Applications of Mathematics
Bifurcations
Boundary value problems
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Original Paper
Parameterization
Polarization
Representations
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Summary: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 S consisting of all bifurcation diagrams with heights. However, we could not find any parameterization of the surface S . In this paper, we show parameterizations of the surface 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.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-022-00537-8