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| We are interesting in wave-pinning in a reaction-diffusion model for cell polarization proposed by Y. Mori, A. Jilkine and L. Edelstein-Keshet in SIAM J. Appl. Math (2011). Wave-pinning means a phenomenon that a wave of activation of one of the species is initiated at one end of the domain, moves into the domain, decelerates, and eventually stops inside the domain, forming a stationary front. Several mathematical bifurcation results of stationary solutions are obtained by Kuto and Tsujikawa in DCDS Supplement (2013). We propose a new method to represent a bifurcation sheet of a shadow-system. It determines the global bifurcation structure of stationary solutions of the shadow-system completely including even secondary bifurcation branches. Moreover, we numerically investigate the global bifurcation structure and stability of the original reaction-diffusion model to understand the wave-pinning. |
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