arXiv 2008.129422020-08nlin.PSmath.DS

三分量FitzHugh-Nagumo模型的行波脉冲解

Traveling pulse solutions in a three-component FitzHugh-Nagumo Model

Takashi Teramoto, Peter van Heijster

摘要：

我们使用几何奇异摄动技术结合行动功能的方法来研究三分量FitzHugh-Nagumo模型中的行波脉冲解。首先，我们导出了具有未知宽度和传播速度的行进$1$脉冲解的轮廓。接下来，我们计算相关联的作用功能，从我们得出的存在条件和鞍结分岔的作用功能及其衍生物的零点。我们通过使用不同的分析方法，利用问题的奇异极限得到相同的条件。我们也适用于这种方法的行动功能的问题旅行$2$脉冲解决方案，并获得明确的存在条件和鞍结分岔。从这些我们推出的必要条件旅行$2$脉冲解的存在。最后，我们讨论了鞍结分岔附近的Hopf分岔。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文