论文标题
在三组分Fitzhugh-Nagumo模型中旅行脉冲解决方案
Traveling pulse solutions in a three-component FitzHugh-Nagumo Model
论文作者
论文摘要
我们使用几何奇异扰动技术与动作功能方法相结合，以研究三组分Fitzhugh-Nagumo模型中的行进脉冲解决方案。首先，我们得出了以不确定的宽度和传播速度的行驶$ 1 $渗透解决方案的轮廓。接下来，我们计算相关的动作功能，从中我们得出了存在的条件，并从中得出了作为动作函数及其衍生物的零的鞍形分叉的条件。我们通过使用不同的分析方法来获得相同的条件，从而利用问题的奇异限制。我们还将操作功能的方法应用于旅行$ 2 $渗透解决方案的问题，并得出存在的明确条件和鞍节分叉。通过这些，我们得出了存在$ 2 $渗透解决方案的必要条件。我们以与鞍节分叉附近的HOPF分叉有关的讨论结束了本文。
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.
