Gröbner Basis Method in FitzHugh-Nagumo Model

HAJNOVÁ, Veronika. Gröbner Basis Method in FitzHugh-Nagumo Model. In C. H. Skiadas and I. Lubashevsky. 11th Chaotic Modeling and Simulation International Conference. Springer Proceedings in Complexity: Springer International Publishing, 2019, p. 77-84. ISBN 978-3-030-15296-3. Available from: https://dx.doi.org/10.1007/978-3-030-15297-0_8.

Basic information

• Original name: Gröbner Basis Method in FitzHugh-Nagumo Model
• Name in Czech: Gröbnerovy báze a FitzHughův-Nagumův Model
• Authors: HAJNOVÁ, Veronika (203 Czech Republic, guarantor, belonging to the institution).
• Edition: Springer Proceedings in Complexity, 11th Chaotic Modeling and Simulation International Conference, p. 77-84, 8 pp. 2019.
• Publisher: Springer International Publishing

Other information

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10102 Applied mathematics
• Country of publisher: Switzerland
• Confidentiality degree: is not subject to a state or trade secret
• Publication form: printed version "print"
• WWW: URL
• RIV identification code: RIV/00216224:14310/19:00109421
• Organization unit: Faculty of Science
• ISBN: 978-3-030-15296-3
• ISSN: 2213-8684
• Doi: http://dx.doi.org/10.1007/978-3-030-15297-0_8
• Keywords (in Czech): FitzHugh-Nagumo model; Gröbner basis; Slow-fast system; Hopf bifurcation; Fold bifurcation
• Keywords in English: FitzHughův-Nagumův model; Gröbnerovy báze; Slow-fast systém; Hopfova bifurkace; Fold bifurkace
• Tags: rivok
• Tags: International impact, Reviewed

Abstract

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.

Links

• MUNI/A/1204/2017, interní kód MU: Name: Matematické statistické modelování 2 (Acronym: MaStaMo2)

Investor: Masaryk University, Category A