A Homoclinic Solution for Excitation Waves on a Contractile Substratum
From MaRDI portal
Publication:4904552
DOI10.1137/12087654XzbMath1260.34080MaRDI QIDQ4904552
Gianni Arioli, Hans Koch, Davide Ambrosi
Publication date: 30 January 2013
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Reaction-diffusion equations (35K57) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Traveling wave solutions (35C07)
Related Items (19)
Parameterization of invariant manifolds for periodic orbits. II: A posteriori analysis and computer assisted error bounds ⋮ Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation ⋮ A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions ⋮ A posteriori error bounds for two point boundary value problems: a Green's function approach ⋮ Phase transition of oscillators and travelling waves in a class of relaxation systems ⋮ A computable criterion for the existence of connecting orbits in autonomous dynamics ⋮ Connecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of Existence ⋮ Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ Computer-Assisted Proof of Shil'nikov Homoclinics: With Application to the Lorenz-84 Model ⋮ Computation of maximal local (un)stable manifold patches by the parameterization method ⋮ Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits ⋮ Resonant tori, transport barriers, and chaos in a vector field with a Neimark-Sacker bifurcation ⋮ Analytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error Bounds ⋮ Study on the Geometrical Properties and Existence of Orbit Homoclinic to a Saddle Point in n-Dimensional Autonomous Vector Field with Polynomials ⋮ Polynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error bounds ⋮ Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation ⋮ Validated computations for connecting orbits in polynomial vector fields ⋮ Existence of Periodic Solutions of the FitzHugh--Nagumo Equations for an Explicit Range of the Small Parameter ⋮ Shilnikov saddle-focus homoclinic orbits from numerics: higher dimensions
This page was built for publication: A Homoclinic Solution for Excitation Waves on a Contractile Substratum
