Work

Bifurcations and Canards in the FitzHugh–Nagumo System: A Tutorial of Fast–Slow Dynamics

Year: 2025

Type: article

Abstract: In this paper, we study the FitzHugh–Nagumo [Formula: see text]-fast–slow system where the vector fields associated to the fast/slow equations come from the reduction of the Hodgkin–Huxley model for the nerve impulse. After deriving the dynamical properties of the singular and regular cases, we perform a bifurcation analysis and investigate how the parameters (of the affine slow equation) impact the dynamics of the system. The study of codimension-1 bifurcations and the numerical locus of canards concludes this case study. All theoretical results are numerically illustrated.

Source: International Journal of Bifurcation and Chaos

DOI: 10.1142/s0218127425300174

Authors: Bruno F. F. Gonçalves, Isabel S. Labouriau, Alexandre A. P. Rodrigues

Institutions: Universidade do Porto, Centro de Matemática, Centro de Matematica Aplicada à Previsão e Decisão Económica

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministério da Ciência, Tecnologia e Ensino Superior, Fundação para a Ciência e a Tecnologia, Centro de Matemática Universidade do Porto