Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System
From MaRDI portal
Publication:2947448
DOI10.1137/140999177zbMath1327.35008OpenAlexW1880775923WikidataQ60143865 ScholiaQ60143865MaRDI QIDQ2947448
Publication date: 24 September 2015
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/4c333a410c4986b1a67faab747c44f7b3e6809b3
Singular perturbations in context of PDEs (35B25) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Blow-up in context of PDEs (35B44) Traveling wave solutions (35C07)
Related Items (33)
Exponential dichotomies for nonlocal differential operators with infinite range interactions ⋮ Instability of small-amplitude periodic waves from fold-Hopf bifurcation ⋮ The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation ⋮ Travelling waves for adaptive grid discretizations of reaction diffusion systems. I: Well-posedness ⋮ Spectra and Stability of Spatially Periodic Pulse Patterns: Evans Function Factorization via Riccati Transformation ⋮ Traveling Stripes in the Klausmeier Model of Vegetation Pattern Formation ⋮ Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities ⋮ Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system ⋮ Global dynamics of an asymmetry piecewise linear differential system: theory and applications ⋮ Reaction-diffusion-advection approach to spatially localized treadmilling aggregates of molecular motors ⋮ Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem ⋮ Existence of traveling wave solutions to reaction-diffusion-ODE systems with hysteresis ⋮ Wiggly canards: growth of traveling wave trains through a family of fast-subsystem foci ⋮ The invariant manifold approach applied to global long-time dynamics of FitzHugh-Nagumo systems ⋮ Qualitative analysis of certain reaction-diffusion systems of the FitzHugh-Nagumo type ⋮ Dynamics of waves and patterns. Abstracts from the workshop held August 8--14, 2021 (hybrid meeting) ⋮ Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System ⋮ Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system ⋮ Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations ⋮ Wave train selection by invasion fronts in the FitzHugh–Nagumo equation ⋮ Spike-adding canard explosion in a class of square-wave bursters ⋮ Stabilities and dynamic transitions of the Fitzhugh-Nagumo system ⋮ Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions ⋮ Near-pulse solutions of the FitzHugh-Nagumo equations on cylindrical surfaces ⋮ Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems ⋮ Traveling Waves for Spatially Discrete Systems of FitzHugh--Nagumo Type with Periodic Coefficients ⋮ Dynamics of the Tyson-Hong-Thron-Novak circadian oscillator model ⋮ Traveling pulses in a coupled FitzHugh-Nagumo equation ⋮ Traveling pulses with oscillatory tails, figure-eight-like stack of isolas, and dynamics in heterogeneous media ⋮ Pulse Replication and Accumulation of Eigenvalues ⋮ A Three-Scale Model of Spatio-Temporal Bursting ⋮ Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations ⋮ Dynamics of $N$-Spot Rings with Oscillatory Tails in a Three-Component Reaction-Diffusion System
Cites Work
- Unnamed Item
- Unnamed Item
- Fast and slow waves in the FitzHugh-Nagumo equation
- Stability of travelling waves with algebraic decay for \(n\)-degree Fisher-type equations
- Exchange lemmas 2: General exchange Lemma
- Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit
- Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations
- Geometric singular perturbation theory for ordinary differential equations
- Differential equations with small parameters and relaxation oscillations. Translation from the Russian by F. M. C. Goodspeed
- A geometric approach to singular perturbation problems with applications to nerve impulse equations
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Existence and Stability of Traveling Pulses in a Neural Field Equation with Synaptic Depression
- Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System
- Traveling Pulse Solutions for the Discrete FitzHugh–Nagumo System
- When Shil'nikov Meets Hopf in Excitable Systems
- Electrical Waves in a One-Dimensional Model of Cardiac Tissue
- Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
- ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
- Tracking Invariant Manifolds up to Exponentially Small Errors
- Stability of pulse solutions for the discrete FitzHugh–Nagumo system
- Relaxation oscillation and canard explosion
This page was built for publication: Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System