Publication details

Gröbner Basis Method in FitzHugh-Nagumo Model

Authors

HAJNOVÁ Veronika

Year of publication 2019
Type Article in Proceedings
Conference 11th Chaotic Modeling and Simulation International Conference
MU Faculty or unit

Faculty of Science

Citation
Web https://www.springer.com/us/book/9783030152963
Doi http://dx.doi.org/10.1007/978-3-030-15297-0_8
Keywords FitzHughův-Nagumův model; Gröbnerovy báze; Slow-fast systém; Hopfova bifurkace; Fold bifurkace
Description The FitzHugh-Nagumo model is a two dimensional system of differential 2 equations with polynomial right-hand sides. The model describes an excitable system 3 and explains basic phenomena in dynamics of neuron activity, for example spike 4 generations in a neuron after stimulation by external current input. The system is 5 slow-fast, meaning system with different time scales for each state variable. We 6 analyse bifurcation manifolds of the FitzHugh-Nagumo system in whole parameter 7 space using algebraic approach based on Gröbner basis.
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