Publication details

Gröbner Basis Method in FitzHugh-Nagumo Model


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

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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