Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
From MaRDI portal
Publication:5687591
DOI10.1098/rsta.1994.0071zbMath0867.35047OpenAlexW2067371846WikidataQ60457709 ScholiaQ60457709MaRDI QIDQ5687591
Kenneth Showalter, Stephen K. Scott, Valery Petrov
Publication date: 20 July 1997
Published in: Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1098/rsta.1994.0071
limit cyclesmultiple steady statesmushroomspurely numerical studysubstantially different diffusion coefficients
Related Items (33)
Axisymmetric ring solutions of the 2D Gray-Scott model and their destabilization into spots ⋮ Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator--prey pursuit and evasion example ⋮ Lattice Boltzmann model for the bimolecular autocatalytic reaction-diffusion equation ⋮ On travelling waves of the Gray–Scott model ⋮ Pulse-pulse interaction in reaction-diffusion systems ⋮ OSCILLATING LOCALIZED STRUCTURES IN REACTION–DIFFUSION SYSTEMS ⋮ Hyperbolic reaction-diffusion equations and irreversible thermodynamics: cubic reversible reaction model ⋮ Homoclinic bifurcations at the onset of pulse self-replication ⋮ PULSE DYNAMICS IN COUPLED EXCITABLE FIBERS: SOLITON-LIKE COLLISION, PHASE LOCKING, AND RECOMBINATION ⋮ Travelling waves in an open cubic autocatalytic system ⋮ A Chebyshev multidomain adaptive mesh method for reaction-diffusion equations ⋮ Asymmetric Spotty Patterns for the Gray-Scott Model in R2 ⋮ Scattering of traveling spots in dissipative systems ⋮ A mathematical mechanism for instabilities in stripe formation on growing domains ⋮ Controlling excitable wave behaviors through the tuning of three parameters ⋮ Dynamics and topological entropy of 1D Greenberg–Hastings cellular automata ⋮ On the back-firing instability ⋮ Instabilities and splitting of pulses in coupled Ginzburg-Landau equations ⋮ \(2^n\)-splitting or edge-splitting? A manner of splitting in dissipative systems ⋮ Nonannihilation dynamics in an exothermic reaction-diffusion system with mono-stable excitability ⋮ Chaotic Wakes and Other Wave-Induced Behavior in a System of Reaction–Diffusion Equations ⋮ The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime ⋮ Motion of pulses and vortices in the cubic-quintic complex Ginzburg-Landau equation without viscosity ⋮ An implicit pseudospectral scheme to solve propagating fronts in reaction-diffusion equations ⋮ Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach ⋮ A skeleton structure of self-replicating dynamics ⋮ Interaction of counterpropagation hot spots in solid fuel combustion ⋮ ON A NONLOCAL EIGENVALUE PROBLEM AND ITS APPLICATIONS TO POINT-CONDENSATIONS IN REACTION–DIFFUSION SYSTEMS ⋮ On a reversible Gray-Scott type system from energetic variational approach and its irreversible limit ⋮ PATTERN DYNAMICS OF A MULTI-COMPONENT REACTION–DIFFUSION SYSTEM: DIFFERENTIATION OF REPLICATING SPOTS ⋮ Turbulence control by wave splitting in excitable media ⋮ Existence and stability of multiple-spot solutions for the Gray-Scott model in \(\mathbb{R}^2\) ⋮ Annihilation of turbulence in excitable systems using pulses that inhibit activator growth
This page was built for publication: Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system