Computational singular perturbation method for the non-standard FitzHugh-Nagumo system
Computational singular perturbation method for the non-standard FitzHugh-Nagumo system
复制标题
非标准FitzHugh-Nagumo系统的计算奇异摄动方法
DOI：
10.1209/0295-5075/ac33ca
复制
发表时间：
2021-10
期刊：
影响因子：
--
通讯作者：
Jürgen Kurths
中科院分区：
文献类型：
--
作者：
Yaru Liu;Shenquan Liu;Jürgen Kurths
构造了一种求解非标准FitzHugh-Nagumo系统的有效计算奇异摄动（CSP）方法，并通过详细的代数分解对其进行了评价。此外，我们的研究还说明了非标准FitzHugh-Nagumo系统具有层和约简问题的几何CSP框架。最后，通过一步和两步CSP更新，介绍了FitzHugh-Nagumo系统的前两个CSP歧管和两个CSP快速光纤。CSP方法可以进一步描述Fenichel流形，有助于更好地理解复杂神经元模型或回路神经模型的动态特性。
Abstract An effective computational singular perturbation (CSP) method for solving the non-standard FitzHugh-Nagumo system is constructed and evaluated by detailed algebra factorization. Furthermore, our studies illustrate a geometric CSP framework with the layer and reduced problems for the non-standard FitzHugh-Nagumo system. Finally, the first two CSP manifolds and two CSP fast fibers are also presented for the FitzHugh-Nagumo system by one-step and two-step CSP updates in this context. The CSP method can further describe Fenichel manifolds and facilitate a better understanding of the dynamic properties of complex neuron models or circuit neural models.