Existence of wavefronts and impulses to FitzHugh-Nagumo equations

DOI10.1016/j.na.2004.03.009zbMath1137.35391OpenAlexW1988330195MaRDI QIDQ1882461

Wenliang Gao, Jinghua Wang

Publication date: 1 October 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.03.009

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Second-order parabolic systems (35K40)

Related Items (10)

A new numerical algorithm for fractional Fitzhugh-Nagumo equation arising in transmission of nerve impulses ⋮ The random attractor of stochastic Fitzhugh-Nagumo equations in an infinite lattice with white noises ⋮ Liouvillian integrability of the FitzHugh-Nagumo systems ⋮ Construction and analysis of some nonstandard finite difference methods for the <scp>FitzHugh–Nagumo</scp> equation ⋮ Stochastic stability of Fitzhugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise ⋮ New results on averaging theory and applications ⋮ Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses ⋮ Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces ⋮ Zero-Hopf bifurcation in the FitzHugh-Nagumo system ⋮ Comparative Study of Some Numerical Methods for the Standard FitzHugh-Nagumo Equation

Cites Work

• Singular perturbation of \(N\)-front travelling waves in the FitzHugh-Nagumo equations
• Propagation Phenomena in a Bistable Reaction-Diffusion System
• The Bifurcations of Countable Connections from a Twisted Heteroclinic Loop
• The Existence of Infinitely Many Traveling Front and Back Waves in the FitzHugh–Nagumo Equations
• ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
• Stability of N-Fronts Bifurcating from a Twisted Heteroclinic Loop and an Application to the Fitzhugh--Nagumo Equation

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