An Invariant Winding Number for the FitzHugh-Nagumo System with Applications to Cardiac Dynamics
An Invariant Winding Number for the FitzHugh-Nagumo System with Applications to Cardiac Dynamics
复制标题
FitzHugh-Nagumo 系统的不变绕数及其在心脏动力学中的应用
DOI：
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发表时间：
2017
影响因子：
2.1
通讯作者：
Kelly M. Paton
中科院分区：
文献类型：
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作者：
E. Cytrynbaum;Kelly M. Paton
FitzHugh-Nagumo（FHN）PDEs系统是可兴奋介质的通用模型，通常用于建立对电生理现象的定性理解。FHN的一个很好的特征化的行进脉冲解决方案可以作为心脏组织和其他环境中动作电位的模型。行进脉冲的稳定性已经得到了很好的研究，但是预测任意初始条件何时收敛到均匀静止解以及何时收敛到行进脉冲的更全局的问题仍然没有解决。在这里，我们证明了存在一个不变的缠绕数的渐近极限的FHN系统称为奇异FHN系统（SFHN），提供了一个关键的一步走向全球收敛的结果。这一结果对于相对一般的非线性是有效的。此外，我们提供的证据表明，我们的SFHN结果扩展与限制FHN和大纲条件下，SFHN近似失败。不变缠绕数提供了解释...
The FitzHugh--Nagumo (FHN) system of PDEs is a generic model for excitable media, often used to build a qualitative understanding of electrophysiological phenomena. A well-characterized traveling pulse solution to FHN serves as a model for action potentials in cardiac tissue and other contexts. The stability of the traveling pulse has been well studied, but the more global problem of predicting when an arbitrary initial condition will converge to the uniform rest solution and when it will converge to the traveling pulse remains unsolved. Here we prove the existence of an invariant winding number in an asymptotic limit of the FHN system called the singular FHN system (SFHN) that provides a crucial step toward a global convergence result. This result is valid for a relatively general class of nonlinearities. In addition, we provide evidence that our SFHN results extend with limitations to FHN and outline conditions under which the SFHN approximation fails. The invariant winding number provides explanations ...
DOI：
10.1146/annurev-bioeng-070909-105305
发表时间：
2010-08-15
影响因子：
9.7
作者：
Dosdall DJ;Fast VG;Ideker RE
通讯作者：
Ideker RE