Heterogeneity-induced effects for pulse dynamics in FitzHugh-Nagumo-type systems
From MaRDI portal
Publication:2000679
DOI10.1016/j.physd.2018.07.001zbMath1415.35162OpenAlexW2860913660WikidataQ129490464 ScholiaQ129490464MaRDI QIDQ2000679
Shyuh-yaur Tzeng, Chao-Nien Chen, Shin-ichiro Ei
Publication date: 28 June 2019
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2018.07.001
Reaction-diffusion equations (35K57) Neural biology (92C20) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)
Related Items (4)
The \(\Gamma\)-limit of traveling waves in the FitzHugh-Nagumo system ⋮ Multiple front standing waves in the FitzHugh-Nagumo equations ⋮ Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical ⋮ Spike solutions for a mass conservation reaction-diffusion system
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dynamics of two interfaces in a hybrid system with jump-type heterogeneity
- Dissipative solitons in reaction diffusion systems. Mechanisms, dynamics, interaction
- Traveling pulse solutions to Fitzhugh-Nagumo equations
- Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimensions
- Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space
- Spikes for the Gierer-Meinhardt system with discontinuous diffusion coefficients
- On the Gierer-Meinhardt system with precursors
- Approximately invariant manifolds and global dynamics of spike states
- Pulse dynamics in a three-component system: Stability and bifurcations
- Pulse dynamics in a three-component system: Existence analysis
- Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations
- Geometric theory of semilinear parabolic equations
- Applications of centre manifold theory
- A positive solution on \(\mathbb{R}^N\) to a system of elliptic equations of FitzHugh-Nagumo type
- Bubbles and droplets in a singular limit of the FitzHugh-Nagumo system
- Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional
- Standing pulse solutions to FitzHugh-Nagumo equations
- Slow-motion manifolds, dormant instability, and singular perturbations
- Dynamics and interactions of spikes on smoothly curved boundaries for reaction-diffusion systems in 2D
- Heterogeneity-induced spot dynamics for a three-component reaction-diffusion system
- Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems
- A variational approach for standing waves of Fitzhugh-Nagumo type systems
- Dynamics of traveling pulses in heterogeneous media of jump type
- Mathematical physiology. I: Cellular physiology
- Traveling waves for the Fitzhugh-Nagumo system on an infinite channel
- Stability analysis for standing pulse solutions to FitzHugh-Nagumo equations
- Maslov index for homoclinic orbits of Hamiltonian systems
- Large stable pulse solutions in reaction-diffusion equations
- Wave-Blocking Phenomena in Bistable Reaction-Diffusion Systems
- Pinned fronts in heterogeneous media of jump type
- Singular Limit Analysis of Stability of Traveling Wave Solutions in Bistable Reaction-Diffusion Systems
- Front Interactions in a Three-Component System
- On the Maslov index of multi-pulse homoclinic orbits
- Dynamics of traveling pulses in heterogeneous media
- Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
- Instability of standing waves for non-linear Schrödinger-type equations
- Stability of multiple-pulse solutions
- The chemical basis of morphogenesis
- Metastable patterns in solutions of ut = ϵ2uxx − f(u)
- Homoclinic Stripe Patterns
- Stability of the in-phase travelling wave solutions in a pair of coupled nerve fibers
- Three Sources and Three Component Parts of the Concept of Dissipative Solitons
- Turing Patterns and Wavefronts for Reaction-Diffusion Systems in an Infinite Channel
- Planar Standing Wavefronts in the FitzHugh--Nagumo Equations
- Interaction of dissipative solitons: Particle-like behaviour of localized structures in a three-component reaction-diffusion system
- The motion of weakly interacting pulses in reaction-diffusion systems
- Standing pulse solutions in reaction-diffusion systems with skew-gradient structure
This page was built for publication: Heterogeneity-induced effects for pulse dynamics in FitzHugh-Nagumo-type systems
