Bifurcation and pattern formation in diffusive Klausmeier-Gray-Scott model of water-plant interaction
DOI10.1016/j.jmaa.2020.124860zbMath1472.35035OpenAlexW3112730456MaRDI QIDQ1996154
Guohong Zhang, Junping Shi, Xiaoli Wang
Publication date: 3 March 2021
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2020.124860
reaction-diffusion modelshadow systemspatial pattern formationsteady state bifurcationwater-plant interaction
Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Plant biology (92C80) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)
Related Items (5)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions
- Analysis of a model for banded vegetation patterns in semi-arid environments with nonlocal dispersal
- Equations of gas combustion: \(S\)-shaped bifurcation and mushrooms
- Monotonicity of the first eigenvalue and the global bifurcation diagram for the branch of interior peak solutions
- Global branch from the second eigenvalue for a semilinear Neumann problem in a ball
- Global branches of non-radially symmetric solutions to a semilinear Neumann problem in a disk
- Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
- On global bifurcation for quasilinear elliptic systems on bounded domains
- Non-existence of non-constant positive steady states of two Holling type-II predator-prey systems: strong interaction case
- Large amplitude stationary solutions to a chemotaxis system
- Diffusion vs cross-diffusion: An elliptic approach
- Locating the peaks of least-energy solutions to a semilinear Neumann problem
- On a nonlocal system for vegetation in drylands
- Vegetation pattern formation in seminal systems due to internal competition reaction between plants
- Bounded components of positive solutions of abstract fixed point equations: Mushrooms, loops and isolas
- The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime
- Diffusion, self-diffusion and cross-diffusion
- Existence and instability of spike layer solutions to singular perturbation problems
- Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. III: The transition between homoclinic solutions
- Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model
- Persistence and bifurcation of degenerate solutions
- Vegetation pattern formation of a water-biomass model
- A fast-slow model of banded vegetation pattern formation in drylands
- Interaction between water and plants: rich dynamics in a simple model
- An analysis of vegetation stripe formation in semi-arid landscapes
- A nonlinear stability analysis of vegetative Turing pattern formation for an interaction-diffusion plant-surface water model system in an arid flat environment
- Some global results for nonlinear eigenvalue problems
- Bifurcation from simple eigenvalues
- Solutions for the Cahn—Hilliard equation with many boundary spike layers
- Pattern Solutions of the Klausmeier Model for Banded Vegetation in Semiarid Environments V: The Transition from Patterns to Desert
- Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments II: patterns with the largest possible propagation speeds
- Pattern solutions of the Klausmeier Model for banded vegetation in semi-arid environments I
- The Existence and Stability of Spike Equilibria in the One‐Dimensional Gray–Scott Model: The Low Feed‐Rate Regime
- Shadow systems and attractors in reaction-diffusion equations
- Global Structure of Bifurcating Solutions of Some Reaction-Diffusion Systems
- On the shape of least‐energy solutions to a semilinear Neumann problem
- Activators and Inhibitors in Pattern Formation
- Existence, stability and metastability of point condensation patterns generated by the Gray-Scott system
- Semilinear Neumann boundary value problems on a rectangle
- The chemical basis of morphogenesis
- Pattern Solutions of the Klausmeier Model for Banded Vegetation in Semiarid Environments IV: Slowly Moving Patterns and Their Stability
- Spatially Periodic Multipulse Patterns in a Generalized Klausmeier--Gray--Scott Model
- Bounds for the Steady-State Sel'kov Model for Arbitrarypin Any Number of Dimensions
- Assessing the robustness of spatial pattern sequences in a dryland vegetation model
- Stationary Pattern of a Ratio-Dependent Food Chain Model with Diffusion
- Pattern formations in two-dimensional Gray-Scott model: Existence of single-spot solutions and their stability
This page was built for publication: Bifurcation and pattern formation in diffusive Klausmeier-Gray-Scott model of water-plant interaction