Gröbner Basis Method in FitzHugh-Nagumo Model
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Proceedings |
| Conference | 11th Chaotic Modeling and Simulation International Conference |
| MU Faculty or unit | |
| 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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