Influence of curvature, growth, and anisotropy on the evolution of Turing patterns on growing manifolds
From MaRDI portal
Publication:2633573
DOI10.1007/s11538-018-0535-yzbMath1415.92034OpenAlexW2903022754WikidataQ90235529 ScholiaQ90235529MaRDI QIDQ2633573
Andrew L. Krause, Meredith A. Ellis, Robert A. van Gorder
Publication date: 9 May 2019
Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11538-018-0535-y
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Developmental biology, pattern formation (92C15)
Related Items (18)
Oscillatory translational instabilities of spot patterns in the Schnakenberg system on general 2D domains ⋮ Control of diffusion-driven pattern formation behind a wave of competency ⋮ Turing and wave instabilities in hyperbolic reaction-diffusion systems: the role of second-order time derivatives and cross-diffusion terms on pattern formation ⋮ Boundary conditions cause different generic bifurcation structures in Turing systems ⋮ Bespoke Turing systems ⋮ Liouville-Green approximation for linearly coupled systems: asymptotic analysis with applications to reaction-diffusion systems ⋮ Growing patterns ⋮ Concentration-dependent domain evolution in reaction-diffusion systems ⋮ Turing patterning in stratified domains ⋮ Pattern formation in reaction-diffusion systems on evolving surfaces ⋮ Turing conditions for pattern forming systems on evolving manifolds ⋮ A hybrid discrete-continuum approach to model Turing pattern formation ⋮ Semi-infinite travelling waves arising in a general reaction–diffusion Stefan model ⋮ Isolating patterns in open reaction-diffusion systems ⋮ Spot patterns of the Schnakenberg reaction–diffusion system on a curved torus ⋮ Global existence of solutions to reaction diffusion systems with mass transport type boundary conditions on an evolving domain ⋮ Analysis of Spot Patterns on a Coordinate-Invariant Model for Vegetation on a Curved Terrain ⋮ Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Pattern formation in reaction-diffusion models with nonuniform domain growth
- Mode transitions in a model reaction-diffusion system driven by domain growth and noise
- Mathematical aspects of pattern formation in biological systems
- Characterization of Turing diffusion-driven instability on evolving domains
- A Turing-Hopf bifurcation scenario for pattern formation on growing domains
- Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains
- The surface finite element method for pattern formation on evolving biological surfaces
- Reaction-diffusion models for biological pattern formation
- The Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function
- Reaction and diffusion on growing domains: scenarios for robust pattern formation
- Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
- Mathematical physiology
- A moving grid finite element method applied to a model biological pattern generator
- Mathematical biology. Vol. 2: Spatial models and biomedical applications.
- Classification of parameter spaces for a reaction-diffusion model on stationary domains
- The effect of growth and curvature on pattern formation
- Stability analysis of Turing patterns generated by the Schnakenberg model
- Complex pattern formation in reaction-diffusion systems with spatially varying parameters
- Bifurcation analysis of reaction-diffusion Schnakenberg model
- Explicitly Solvable Nonlocal Eigenvalue Problems and the Stability of Localized Stripes in Reaction-Diffusion Systems
- The dynamics of localized spot patterns for reaction-diffusion systems on the sphere
- Stripes or spots? Nonlinear effects in bifurcation of reaction—diffusion equations on the square
- Finite elements on evolving surfaces
- Patterns on growing square domains via mode interactions
- The chemical basis of morphogenesis
- History dependence and the continuum approximation breakdown: the impact of domain growth on Turing’s instability
- Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces
- Simple computation of reaction–diffusion processes on point clouds
- A Trace Finite Element Method for PDEs on Evolving Surfaces
- Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems
- Pattern formation outside of equilibrium
- An Extension of Chebfun to Two Dimensions
- Finite element methods for surface PDEs
- Computing with Functions in Spherical and Polar Geometries I. The Sphere
- Turing instabilities in general systems
This page was built for publication: Influence of curvature, growth, and anisotropy on the evolution of Turing patterns on growing manifolds
