SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2194-2231, January 2020.
We rigorously prove the existence of traveling fronts in neural field models with lateral inhibition coupling types and smooth sigmoidal firing rates. With Heaviside firing rates as our base point (where unique traveling fronts exist), we repeatedly apply the implicit function theorem in Banach spaces to provide a nonmonotone version of the homotopy approach originally proposed by Ermentrout and McLeod [Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 461--478] in their seminal study of monotone fronts in purely excitatory models. By comparing smooth and Heaviside firing rates, we develop global wave speed and profile comparisons that guide our analysis, leading to uniqueness (modulo translation) in the perturbative case. Moreover, we establish a meaningful a priori existence result; we prove existence holds for a range of firing rates, independent of continuation path.

中文翻译：

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具有S形发射率的侧向抑制神经场的行进前沿的存在与唯一性。

SIAM应用动力系统杂志，第19卷第3期，第2194-2231页，2020年1月。
我们严格证明了神经场模型中具有横向抑制耦合类型和平滑的S形点火速率的行进前沿的存在。以Heaviside发射速率为基点（存在独特的行进前沿），我们在Banach空间中反复应用隐函数定理，以提供Ermentrout和McLeod [Proc。罗伊 Soc。爱丁堡教派。A，123（1993），pp。461--478]在纯兴奋性模型中对单调前沿的开创性研究中。通过比较平滑和较重的发射速率，我们开发了整体波速和轮廓比较，以指导我们的分析，从而在扰动情况下实现了唯一性（模转换）。此外，我们建立了有意义的先验存在结果；我们证明了存在对于一系列的发射率来说是成立的