Turing Pattern Formation in the Brusselator Model with Superdiffusion

DOI10.1137/070703454zbMath1170.35053OpenAlexW2061393260MaRDI QIDQ3614144

A. A. Golovin, Vladimir A. Volpert, Bernard J. Matkowsky

Publication date: 16 March 2009

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

Full work available at URL: https://doi.org/10.1137/070703454

zbMATH Keywords

stability boundarieslinear stability analysissuperdiffusionanomalous diffusionTuring instabilityweakly nonlinear analysisself-replicating spots

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Developmental biology, pattern formation (92C15) Bifurcations in context of PDEs (35B32)

Related Items (52)

Stability analysis in a diffusional immunosuppressive infection model with delayed antiviral immune response ⋮ Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain ⋮ Turing Pattern Dynamics in an SI Epidemic Model with Superdiffusion ⋮ Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model ⋮ A cubic autocatalator chemical reaction model with limit cycle analysis and consistency preserving discretization ⋮ Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting ⋮ Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack ⋮ Bifurcation analysis of a diffusive predator-prey model with ratio-dependent Holling type III functional response ⋮ Nonlinear stability analyses of vegetative pattern formation in an arid environment ⋮ Bistability and Turing pattern induced by cross fraction diffusion in a predator-prey model ⋮ Turing-Hopf bifurcation analysis in a superdiffusive predator-prey model ⋮ Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion ⋮ Pattern formation of a diffusive predator-prey model with strong allee effect and nonconstant death rate ⋮ Patterns of a superdiffusive consumer-resource model with hunting cooperation functional response ⋮ Analysis and pattern formation scenarios in the superdiffusive system of predation described with Caputo operator ⋮ Chaotic dynamics in Bonhoffer-van der Pol fractional reaction-diffusion system ⋮ Complex pattern formation arising from wave instabilities in a three-agent chemical system with superdiffusion ⋮ Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion ⋮ Turing instability and pattern formation for the Lengyel-Epstein system with nonlinear diffusion ⋮ Existence and stability of symmetric and asymmetric patterns for the half-Laplacian Gierer–Meinhardt system in one-dimensional domain ⋮ Pattern selection in ternary mushy layers ⋮ Pattern formation of Brusselator in the reaction-diffusion system ⋮ Turing Patterns in the Lengyel–Epstein System with Superdiffusion ⋮ Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system ⋮ Global existence and large time behavior of solutions of a time fractional reaction diffusion system ⋮ Dynamic analysis of a diffusive predator-prey model with hunting cooperation functional response and prey-taxis ⋮ A nonlinear stability analysis of vegetative Turing pattern formation for an interaction-diffusion plant-surface water model system in an arid flat environment ⋮ Spike solutions to the supercritical fractional Gierer-Meinhardt system ⋮ An effective analytical method for fractional Brusselator reaction–diffusion system ⋮ Turing pattern formation in a semiarid vegetation model with fractional-in-space diffusion ⋮ Spatiotemporal Patterns Induced by Cross-Diffusion in a Three-Species Food Chain Model ⋮ Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains ⋮ A novel chaos control strategy for discrete-time Brusselator models ⋮ SPATIOTEMPORAL DYNAMICS OF A DIFFUSIVE LESLIE-TYPE PREDATOR–PREY MODEL WITH BEDDINGTON–DEANGELIS FUNCTIONAL RESPONSE ⋮ Turing instability of Brusselator in the reaction-diffusion network ⋮ Local discontinuous Galerkin methods coupled with implicit integration factor methods for solving reaction-cross-diffusion systems ⋮ Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion ⋮ Multi-bump ground states of the fractional Gierer-Meinhardt system on the real line ⋮ Pattern formation by super-diffusion in Fitzhugh-Nagumo model ⋮ Hopf bifurcation in a fractional diffusion food-limited models with feedback control ⋮ Lattice Boltzmann simulation of pattern formation under cross-diffusion ⋮ Pattern formation of a coupled two-cell Brusselator model ⋮ Spatiotemporal dynamics induced by delay and diffusion in a predator-prey model with mutual interference among the predator ⋮ Mathematical modeling of different types of instabilities in time fractional reaction-diffusion systems ⋮ Front dynamics in a two-species competition model driven by Lévy flights ⋮ Pattern formation by fractional cross-diffusion in a predator–prey model with Beddington–DeAngelis type functional response ⋮ Mathematical modelling of pattern formation in activator-inhibitor reaction-diffusion systems with anomalous diffusion ⋮ Interaction of Turing and Hopf modes in the superdiffusive Brusselator model ⋮ Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains ⋮ Bifurcation Analysis of a Diffusive Predator–Prey Model with Bazykin Functional Response ⋮ Two different approaches for parameter identification in a spatial-temporal rumor propagation model based on Turing patterns ⋮ Spatiotemporal Dynamics of a Diffusive Leslie–Gower Predator–Prey Model with Ratio-Dependent Functional Response

This page was built for publication: Turing Pattern Formation in the Brusselator Model with Superdiffusion