Turning points and traveling waves in Fitzhugh--Nagumo type equations

DOI10.1016/j.jde.2005.10.006zbMath1103.34031OpenAlexW2063545395MaRDI QIDQ2496732

Erik S. Van Vleck, Weishi Liu

Publication date: 20 July 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2005.10.006

zbMATH Keywords

turning pointtraveling waveexchange Lemma

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (18)

Viscous singular shock profiles for a system of conservation laws modeling two-phase flow ⋮ The existence of solitary wave solutions of delayed Camassa-Holm equation via a geometric approach ⋮ Phase transition of oscillators and travelling waves in a class of relaxation systems ⋮ Geometric singular perturbations for multiple turning points: invariant manifolds and exchange lemmas ⋮ Traveling pulses of coupled Fitzhugh-Nagumo equations with doubly-diffusive effect ⋮ Physical-bound-preserving finite volume methods for the Nagumo equation on distorted meshes ⋮ Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation ⋮ A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations ⋮ A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation ⋮ The existence and asymptotic estimates of solutions for a third-order nonlinear singularly perturbed boundary value problem ⋮ Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces ⋮ Invariant algebraic surfaces of the FitzHugh-Nagumo system ⋮ Dynamics of traveling waves for the perturbed generalized KdV equation ⋮ On the global dynamics of the Newell–Whitehead system ⋮ Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation ⋮ Diversity of traveling wave solutions in Fitzhugh-Nagumo type equations ⋮ Solitary wave solutions of delayed coupled Higgs field equation ⋮ Positivity preserving finite volume scheme for the Nagumo-type equations on distorted meshes

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