Pattern selection in the 2D FitzHugh-Nagumo model

DOI10.1007/s11587-018-0424-6zbMath1431.37059OpenAlexW2893227892MaRDI QIDQ2281533

Gianfranco Rubino, Marco Sammartino, Gaetana Gambino, Maria Carmela Lombardo

Publication date: 3 January 2020

Published in: Ricerche di Matematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11587-018-0424-6

zbMATH Keywords

square patternsamplitude equationsTuring instabilityFitzHugh-Nagumo model

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Pattern formations in context of PDEs (35B36)

Related Items (13)

Abundant distinct types of solutions for the nervous biological fractional FitzHugh-Nagumo equation via three different sorts of schemes ⋮ Multilinear POD-DEIM model reduction for 2D and 3D semilinear systems of differential equations ⋮ A computationally efficient strategy for time-fractional diffusion-reaction equations ⋮ Subcritical Turing patterns in hyperbolic models with cross-diffusion ⋮ Turing instability induced by random network in FitzHugh-Nagumo model ⋮ Adaptive POD-DEIM correction for Turing pattern approximation in reaction-diffusion PDE systems ⋮ Localized model order reduction and domain decomposition methods for coupled heterogeneous systems ⋮ A priori estimates for solutions of FitzHugh-Rinzel system ⋮ A second order directional split exponential integrator for systems of advection-diffusion-reaction equations ⋮ A generalized Degn-Harrison reaction-diffusion system: asymptotic stability and non-existence results ⋮ On solutions to a FitzHugh-Rinzel type model ⋮ On pattern formation in reaction-diffusion systems containing self- and cross-diffusion ⋮ Cross-diffusion effects on stationary pattern formation in the Fitzhugh-Nagumo model

Cites Work

• Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model
• On a cross-diffusion population model deduced from mutation and splitting of a single species
• Turing instability and pattern formation for the Lengyel-Epstein system with nonlinear diffusion
• Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
• About reaction-diffusion systems involving the Holling-type II and the Beddington-DeAngelis functional responses for predator-prey models
• \(L^2\)-energy decay of convective nonlinear PDEs reaction-diffusion systems via auxiliary ODEs systems
• Snakes and ladders: localized states in the Swift-Hohenberg equation
• Axisymmetric cellular structures revisited
• Simulation, modeling, and analysis of soliton waves interaction and propagation in CNN transmission lines for innovative data communication and processing
• Pattern formation by super-diffusion in Fitzhugh-Nagumo model
• Pattern formation driven by cross-diffusion in a 2D domain
• Pattern formation in the FitzHugh-Nagumo model
• Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth
• Wave features of a hyperbolic reaction-diffusion model for chemotaxis
• Pattern formation and modulation in a hyperbolic vegetation model for semiarid environments
• Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion
• Demyelination patterns in a mathematical model of multiple sclerosis
• Square Turing patterns in reaction-diffusion systems with coupled layers
• Approximated Spiral and Target Patterns in Bazykin’s Prey–Predator Model: Multiscale Perturbation Analysis
• Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion
• The Method of Normal Forms
• Solitary waves in excitable systems with cross-diffusion
• Nonlinear Dynamic Stability: A Formal Theory
• Equilibria, stability and excitability in a general class of plankton population models

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