Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model
DOI10.1007/s10884-018-9694-7zbMath1415.35018OpenAlexW2887850585WikidataQ129405014 ScholiaQ129405014MaRDI QIDQ1739077
Yasumasa Nishiura, Takashi Teramoto, Peter van Heijster, Chao-Nien Chen
Publication date: 25 April 2019
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10884-018-9694-7
pulse solutionslocalised defect solutionspinned front solutionspinning distancesmall jump-type heterogeneity
Variational inequalities (49J40) Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Nonlinear ordinary differential equations and systems (34A34) Discontinuous ordinary differential equations (34A36) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dynamics of two interfaces in a hybrid system with jump-type heterogeneity
- Unstable gap solitons in inhomogeneous nonlinear Schrödinger equations
- Traveling pulse solutions to Fitzhugh-Nagumo equations
- Planar radial spots in a three-component FitzHugh-Nagumo system
- Steady-state autowave patterns in a two-dimensional excitable medium with a band of different excitability
- Stability of stationary fronts in a non-linear wave equation with spatial inhomogeneity
- Spikes for the Gierer-Meinhardt system with discontinuous diffusion coefficients
- Pulse dynamics in a three-component system: Stability and bifurcations
- Pulse dynamics in a three-component system: Existence analysis
- Geometric singular perturbation theory for ordinary differential equations
- Diffusion driven instability in an inhomogeneous domain
- Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional
- Standing pulse solutions to FitzHugh-Nagumo equations
- Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach
- Existence and multiplicity results for heteroclinic orbits of second order Hamiltonian systems
- Slow-motion manifolds, dormant instability, and singular perturbations
- Front dynamics in heterogeneous diffusive media
- Butterfly catastrophe for fronts in a three-component reaction-diffusion system
- Multiple front standing waves in the FitzHugh-Nagumo equations
- On bifurcation from infinity
- Stability of fronts in inhomogeneous wave equations
- A variational approach for standing waves of Fitzhugh-Nagumo type systems
- Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system
- Stability analysis for standing pulse solutions to FitzHugh-Nagumo equations
- Maslov index for homoclinic orbits of Hamiltonian systems
- Practical bifurcation and stability analysis
- Large stable pulse solutions in reaction-diffusion equations
- A stability index analysis of 1-D patterns of the Gray-Scott model
- A Geometric Approach to Stationary Defect Solutions in One Space Dimension
- First and Second Order Semistrong Interaction in Reaction-Diffusion Systems
- Robust Pulse Generators in an Excitable Medium with Jump-Type Heterogeneity
- Sustained Resonance for a Nonlinear System with Slowly Varying Coefficients
- Pinned fronts in heterogeneous media of jump type
- The Dynamics and Pinning of a Spike for a Reaction-Diffusion System
- Front Interactions in a Three-Component System
- Dynamics of traveling pulses in heterogeneous media
- Localized patterns in reaction-diffusion systems
- Metastable patterns in solutions of ut = ϵ2uxx − f(u)
- A Renormalization Method for Modulational Stability of Quasi-Steady Patterns in Dispersive Systems
- Localized standing waves in inhomogeneous Schrödinger equations
- Pinned fluxons in a Josephson junction with a finite-length inhomogeneity
- Planar Standing Wavefronts in the FitzHugh--Nagumo Equations
- Stability Criteria for Reaction-Diffusion Systems with Skew-Gradient Structure
- Interaction of dissipative solitons: Particle-like behaviour of localized structures in a three-component reaction-diffusion system
- Periodic solutions and their connecting orbits of Hamiltonian systems.