Butterfly catastrophe for fronts in a three-component reaction-diffusion system

DOI10.1007/s00332-014-9222-9zbMath1325.35088OpenAlexW2085170514MaRDI QIDQ2018851

Martina Chirilus-Bruckner, Arjen Doelman, Peter van Heijster, Jens D. M. Rademacher

Publication date: 25 March 2015

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-014-9222-9

zbMATH Keywords

Evans functionFitzHugh-Nagumo modelsingular perturbation theorycenter-manifold reduction

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25) Bifurcations in context of PDEs (35B32) Pattern formations in context of PDEs (35B36)

Related Items (12)

The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation ⋮ Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional ⋮ Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system ⋮ Reduction approach to the dynamics of interacting front solutions in a bistable reaction-diffusion system and its application to heterogeneous media ⋮ Reaction–diffusion fronts and the butterfly set ⋮ Matched asymptotic expansion approach to pulse dynamics for a three-component reaction-diffusion system ⋮ Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model ⋮ Competing ternary surface reaction CO + O ₂  + H ₂ on Ir(111) ⋮ Multichromatic travelling waves for lattice Nagumo equations ⋮ Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system ⋮ A Geometric Approach to Stationary Defect Solutions in One Space Dimension ⋮ Traveling Pulse Solutions in a Three-Component FitzHugh--Nagumo Model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Planar radial spots in a three-component FitzHugh-Nagumo system
• Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
• Dynamics of front solutions in a specific reaction-diffusion system in one dimension
• Pulse dynamics in a three-component system: Stability and bifurcations
• Pulse dynamics in a three-component system: Existence analysis
• Geometric theory of semilinear parabolic equations
• Pulse-pulse interaction in reaction-diffusion systems
• Absolute and convective instabilities of waves on unbounded and large bounded domains
• Standing pulse solutions to FitzHugh-Nagumo equations
• Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach
• Slow-motion manifolds, dormant instability, and singular perturbations
• Evans function and blow-up methods in critical eigenvalue problems
• On large ring solutions for Gierer-Meinhardt system in \(\mathbb R^3\)
• Heteroclinic and homoclinic bifurcations in bistable reaction diffusion systems
• Slowly Modulated Two-Pulse Solutions in the Gray--Scott Model II: Geometric Theory, Bifurcations, and Splitting Dynamics
• Large stable pulse solutions in reaction-diffusion equations
• A stability index analysis of 1-D patterns of the Gray-Scott model
• First and Second Order Semistrong Interaction in Reaction-Diffusion Systems
• Zigzag and Breakup Instabilities of Stripes and Rings in the Two‐Dimensional Gray–Scott Model
• Front Interactions in a Three-Component System
• Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model
• Dynamics of traveling pulses in heterogeneous media
• Localized patterns in reaction-diffusion systems
• Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• A Renormalization Method for Modulational Stability of Quasi-Steady Patterns in Dispersive Systems
• Adiabatic stability under semi-strong interactions: The weakly damped regime
• Nonlinear Asymptotic Stability of the Semistrong Pulse Dynamics in a Regularized Gierer–Meinhardt Model
• The Slow Dynamics of Two-Spike Solutions for the Gray--Scott and Gierer--Meinhardt Systems: Competition and Oscillatory Instabilities
• Spatio-temporal chaos for the Gray-Scott model
• The motion of weakly interacting pulses in reaction-diffusion systems

This page was built for publication: Butterfly catastrophe for fronts in a three-component reaction-diffusion system