发表机构
Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过构造耦合上下解，为异质FitzHugh--Nagumo系统提供传播失败的充分条件，并建立方向性信号阻断，适用于神经元模型。
AI 中文摘要
行波是反应-扩散系统中的基本对象；然而，空间异质性会扭曲或抑制其传播。确定给定的异质性是否导致传播失败仍然具有挑战性，尤其是在具有耦合组件的系统中。在本文中，我们针对一维FitzHugh--Nagumo系统，为特定异质性构造了显式的平稳耦合上下解。通过利用系统的混合拟单调结构，这些屏障为一系列受困初始条件的传播失败提供了充分条件。平稳构造在具有局部抑制动力学或急剧几何变化的FitzHugh--Nagumo神经元模型中建立了方向性信号阻断，并且所得的平稳屏障在恢复扩散足够小的情况下持续存在。此外，我们引入了显式的几乎平稳屏障，其为均匀介质中分量阈值区域的扩展提供了条件性界限。
英文摘要
Traveling waves are fundamental objects in reaction--diffusion systems; however, spatial heterogeneities can distort or inhibit their propagation. Determining whether a given heterogeneity results in propagation failure remains challenging, particularly in systems with coupled components. In this paper, we present explicit constructions of stationary coupled upper and lower solutions tailored to specific heterogeneities for a one-dimensional FitzHugh--Nagumo system. By leveraging the mixed quasimonotone structure of the system, these barriers yield sufficient conditions for the failure of propagation for families of trapped initial conditions. The stationary constructions establish directional signal blocking in FitzHugh--Nagumo neuron models with localized depressed dynamics or abrupt geometric variations, and the resulting stationary barriers persist for sufficiently small recovery diffusion. Additionally, we introduce explicit almost stationary barriers, which provide conditional bounds on the expansion of componentwise threshold regions in homogeneous media.
Comments34 pages, 7 figures
