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Computational singular perturbation method for the non-standard FitzHugh-Nagumo system

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Liu,  Yaru
External Organizations;

Liu,  Shenquan
External Organizations;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Liu, Y., Liu, S., Kurths, J. (2022): Computational singular perturbation method for the non-standard FitzHugh-Nagumo system. - EPL (Europhysics Letters), 139, 3, 32002.
https://doi.org/10.1209/0295-5075/ac33ca


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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.