Traveling Pulse Solutions in a Three-Component FitzHugh--Nagumo Model

DOI10.1137/20M1334942zbMath1462.35038arXiv2008.12942MaRDI QIDQ4983535

Peter van Heijster, Takashi Teramoto

Publication date: 20 April 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.12942

zbMATH Keywords

saddle-node bifurcationreaction-diffusion systemsHopf bifurcationsaction functionalsingular limittraveling 1-pulse solutionstraveling 2-pulse solutions

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (2)

Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system ⋮ Arbitrarily weak head-on collision can induce annihilation: the role of hidden instabilities

Cites Work

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• Dynamics of two interfaces in a hybrid system with jump-type heterogeneity
• Traveling pulse solutions to Fitzhugh-Nagumo equations
• Planar radial spots in a three-component FitzHugh-Nagumo system
• Pulse dynamics in a three-component system: Stability and bifurcations
• Pulse dynamics in a three-component system: Existence analysis
• Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional
• Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model
• Standing pulse solutions to FitzHugh-Nagumo equations
• Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach
• Spectral and dynamical stability of nonlinear waves
• Heterogeneity-induced spot dynamics for a three-component reaction-diffusion system
• On a variational problem arising from the three-component FitzHugh-Nagumo type reaction-diffusion systems
• Butterfly catastrophe for fronts in a three-component reaction-diffusion system
• Reduction approach to the dynamics of interacting front solutions in a bistable reaction-diffusion system and its application to heterogeneous media
• Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system
• A steepest descent algorithm for the computation of traveling dissipative solitons
• Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain
• The \(\Gamma\)-limit of traveling waves in the FitzHugh-Nagumo system
• 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
• Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems
• Scattering of traveling spots in dissipative systems
• Front Interactions in a Three-Component System
• Localized patterns in reaction-diffusion systems
• Stability of Singularly Perturbed Solutions to Systems of Reaction-Diffusion Equations
• Spatially localized structures in dissipative systems: open problems
• Wave solutions to reaction-diffusion systems in perforated domains
• Interaction of dissipative solitons: Particle-like behaviour of localized structures in a three-component reaction-diffusion system

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