Dynamic transitions of the Fitzhugh-Nagumo equations on a finite domain

DOI10.3934/DCDSB.2018118zbMath1406.35436OpenAlexW2796569373MaRDI QIDQ1756861

Yiqiu Mao

Publication date: 27 December 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018118

zbMATH Keywords

Hopf bifurcationphase transition dynamicsFitzhugh-Nagumo modelcenter manifold reductionimpulse trains

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Biochemistry, molecular biology (92C40) Bifurcations in context of PDEs (35B32)

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Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food ⋮ Stability and dynamic transition of vegetation model for flat arid terrains ⋮ Dynamic transitions and bifurcations of 1D reaction–diffusion equations: The self‐adjoint case ⋮ Stabilities and dynamic transitions of the Fitzhugh-Nagumo system ⋮ Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron

Cites Work

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• Fast and slow waves in the FitzHugh-Nagumo equation
• Mathematical foundations of neuroscience
• Geometric theory of semilinear parabolic equations
• Attractor bifurcation theory and its applications to Rayleigh-Bénard convection
• Phase Transition Dynamics
• Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
• ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
• Perturbation analysis of an approximation to the Hodgkin-Huxley theory

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