Multiple-peak traveling waves of the Gray-Scott model

Periodic solutions to ordinary differential equations (34C25) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Reaction-diffusion equations (35K57) Classical flows, reactions, etc. in chemistry (92E20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Traveling wave solutions (35C07)

Cites Work

Existence of traveling waves of auto-catalytic systems with decay
Steady states and dynamics of an autocatalytic chemical reaction model with decay
Hair-triggered instability of radial steady states, spread and extinction in semilinear heat equations
Homoclinic bifurcations at the onset of pulse self-replication
The approach of solutions of nonlinear diffusion equations to travelling front solutions
Dynamics of a periodically pulsed bio-reactor model
Pulse-pulse interaction in reaction-diffusion systems
Traveling waves in a convolution model for phase transitions
Traveling waves for a biological reaction-diffusion model
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime
Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach
Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system
Stability and instability in the Gray-Scott model: The case of equal diffusivities
Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity
Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission
Traveling waves in a bio-reactor model
Slowly modulated two-pulse solutions in the Gray--Scott model. II: Geometric theory, bifurcations, and splitting dynamics
Stability of Traveling Front Solutions with Algebraic Spatial Decay for Some Autocatalytic Chemical Reaction Systems
Existence of traveling waves in a simple isothermal chemical system with the same order for autocatalysis and decay
The Stability and Dynamics of Localized Spot Patterns in the Two-Dimensional Gray–Scott Model
Stability of the Static Spike Autosolitons in the Gray--Scott Model
Traveling waves of two-component reaction-diffusion systems arising from higher order autocatalytic models
Asymmetric Spotty Patterns for the Gray-Scott Model in R2
Propagation of Local Disturbances in Reaction Diffusion Systems Modeling Quadratic Autocatalysis
The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves
Effects of Random Motility on Microbial Growth and Competition in a Flow Reactor
The global dynamics of isothermal chemical systems with critical nonlinearity
Exact Homoclinic and Heteroclinic Solutions of the Gray--Scott Model for Autocatalysis
Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations
Qualitative analysis of an autocatalytic chemical reaction model with decay
The global self-similarity of a chemical reaction system with critical nonlinearity
Sharp Estimates on Minimum Travelling Wave Speed of Reaction Diffusion Systems Modelling Autocatalysis
Traveling spike autosolitons in the Gray-Scott model

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