Traveling pulse solutions in a three-component FitzHugh-Nagumo model
Traveling pulse solutions in a three-component FitzHugh-Nagumo model
复制标题
三分量 FitzHugh-Nagumo 模型中的行进脉冲解决方案
DOI：
10.1137/20m1334942
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发表时间：
2021
影响因子：
2.1
通讯作者：
Peter van Heijster
中科院分区：
文献类型：
--
作者：
Takashi Teramoto;Peter van Heijster
我们使用几何奇异摄动技术与动作泛函方法相结合来研究三分量 FitzHugh-Nagumo 模型中的行进脉冲解。首先，我们推导出宽度和传播速度不确定的行进 1 脉冲解的轮廓。接下来，我们计算该轮廓的相关动作泛函，从中导出存在条件和鞍节点分叉作为动作泛函及其导数的零点。我们通过使用不同的分析方法来利用问题的奇异极限，从而获得相同的条件。我们还将这种作用泛函方法应用于行进 2 脉冲解的问题，并推导出存在和鞍节点分岔的显式条件。由此我们推导出行进 2 脉冲解存在的必要条件。我们以与鞍节点分岔附近的 Hopf 分岔相关的讨论来结束本文。 （附有更正版本。）
We use geometric singular perturbation techniques combined with an action functional approach to study traveling pulse solutions in a three-component FitzHugh--Nagumo model. First, we derive the profile of traveling 1-pulse solutions with undetermined width and propagating speed. Next, we compute the associated action functional for this profile from which we derive the conditions for existence and a saddle-node bifurcation as the zeros of the action functional and its derivatives. We obtain the same conditions by using a different analytical approach that exploits the singular limit of the problem. We also apply this methodology of the action functional to the problem for traveling 2-pulse solutions and derive the explicit conditions for existence and a saddle-node bifurcation. From these we deduce a necessary condition for the existence of traveling 2-pulse solutions. We end this article with a discussion related to Hopf bifurcations near the saddle-node bifurcation. (A corrected version is attached.)