Existence, Stability, and Dynamics of Ring and Near-Ring Solutions to the Saturated Gierer--Meinhardt Model in the Semistrong Regime
نویسندگان
چکیده
منابع مشابه
Existence, Stability, and Dynamics of Ring and Near-Ring Solutions to the Saturated Gierer-Meinhardt Model in the Semistrong Regime
We analyze a singularly perturbed reaction-diffusion system in the semi-strong diffusion regime in two spatial dimensions where an activator species is localized to a closed curve, while the inhibitor species exhibits long range behavior over the domain. In the limit of small activator diffusivity we derive a new moving boundary problem characterizing the slow time evolution of the curve, which...
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We analyze a singularly perturbed reaction-diffusion system in the semi-strong diffusion regime in two spatial dimensions where an activator species is localized to a closed curve, while the inhibitor species exhibits long range behavior over the domain. In the limit of small activator diffusivity we derive a new moving boundary problem characterizing the slow time evolution of the curve, which...
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We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semi-strong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semi-strong limit the localized activator pulses interact strongly through the slowly varying inhibitor. The interaction is not tail-tail as in the weak interaction limit, and the pulse amplitudes and speed...
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with an additional restriction q = p − 1. In the limit ε → 0, we use formal asymptotics to construct a solution whose activator component a concentrates on a circle. Under additional constraints p > 1, m > 0, and 1 < m − s < 3, we find that such a solution exists and is unique. The radius of the circle of concentration is given explicitly in terms of certain integrals. Full numerical computatio...
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Abstract. We consider the steady states of the Gierer–Meinhardt system on all of R: εΔa − a + a hq = 0, Δh − h + a hs = 0 with an additional restriction q = p − 1. In the limit ε → 0, we use formal asymptotics to construct a solution whose activator component a concentrates on a circle. Under the additional constraints p > 1, m > 0, and 1 < m− s < 3, we find that such a solution exists and is u...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2017
ISSN: 1536-0040
DOI: 10.1137/16m1060327