| Issue |
EPL
Volume 139, Number 3, August 2022
|
|
|---|---|---|
| Article Number | 32002 | |
| Number of page(s) | 6 | |
| Section | Mathematical and interdisciplinary physics | |
| DOI | https://doi.org/10.1209/0295-5075/ac33ca | |
| Published online | 01 August 2022 | |
Computational singular perturbation method for the non-standard FitzHugh-Nagumo system
1 School of Mathematics, South China University of Technology - Guangzhou 510640, China
2 Potsdam Institute for Climate Impact Research - Potsdam 14473, Germany
3 Department of Physics, Humboldt University of Berlin - Berlin 12489, Germany
(a) mashqliu@scut.edu.cn (corresponding author)
Received: 8 March 2021
Accepted: 27 October 2021
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.
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