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Global bifurcation sheet and diagrams of wave-pinning in a reaction-diffusion model for cell polarization
| 1. | Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194, Japan |
| 2. | Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585 |
| 3. | Research Institute for Electronic Science, Hokkaido University, CREST, Japan Science and Technology Agency, N12W7, Kita-Ward, Sapporo, 060-0812, Japan |
| 4. | Faculty of Engineering, University of Miyazaki, Miyazaki, 889-2192 |
| 5. | Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, Shiga 520-2194 |
References:
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J. Carr, M. E. Gurtin, and M. Semrod, Structured phase transitions on a finite interval,, Arch. Rational Mech. Anal., 86 (1984), 317.
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J. Smoller and A.Wasserman, Global bifurcation of steady-state solutions,, J. Differential Equations, 39 (1981), 269.
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J. Smoller, Shock Waves and Reaction Diffusion Equations,, Springer, (1994).
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K. Kuto and T. TsujikawaE, Bifurcation structure of steady-states for bistable equations with nonlocal constraint,, Discrete and Continuous Dynamical Systems Supplement, (2013), 467. |
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S.KosugiE Y. Morita, and S. YotsutaniE, Stationary solutions to the one-dimensional Cahn-Hilliard equation: Proof by the complete elliptic integrals,, Discrete and Continuous Dynamical Systems, 19 (2007), 609.
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Y.Lou, W-M.Ni and S.Yotsutani, On a limiting system in the Lotka-Voltera competition with cross diffusion,, Discrete Contin. Dyn. Syst., 10 (2004), 435.
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| [7] |
Y.Mori, A.Jilkine and L.Edelstein-Keshet, Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization, SIAM JE ApplE Math., 71 (2011), 1401.
|
show all references
References:
| [1] |
J. Carr, M. E. Gurtin, and M. Semrod, Structured phase transitions on a finite interval,, Arch. Rational Mech. Anal., 86 (1984), 317.
|
| [2] |
J. Smoller and A.Wasserman, Global bifurcation of steady-state solutions,, J. Differential Equations, 39 (1981), 269.
|
| [3] |
J. Smoller, Shock Waves and Reaction Diffusion Equations,, Springer, (1994).
|
| [4] |
K. Kuto and T. TsujikawaE, Bifurcation structure of steady-states for bistable equations with nonlocal constraint,, Discrete and Continuous Dynamical Systems Supplement, (2013), 467. |
| [5] |
S.KosugiE Y. Morita, and S. YotsutaniE, Stationary solutions to the one-dimensional Cahn-Hilliard equation: Proof by the complete elliptic integrals,, Discrete and Continuous Dynamical Systems, 19 (2007), 609.
|
| [6] |
Y.Lou, W-M.Ni and S.Yotsutani, On a limiting system in the Lotka-Voltera competition with cross diffusion,, Discrete Contin. Dyn. Syst., 10 (2004), 435.
|
| [7] |
Y.Mori, A.Jilkine and L.Edelstein-Keshet, Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization, SIAM JE ApplE Math., 71 (2011), 1401.
|
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