Global well-posedness, pattern formation and spiky stationary solutions in a Beddington-DeAngelis competition system
DOI10.3934/dcds.2020108zbMath1436.35030OpenAlexW3000091528MaRDI QIDQ1988306
Ling Jin, Qi Wang, Zengyan Zhang
Publication date: 16 April 2020
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcds.2020108
Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Population dynamics (general) (92D25) Ecology (92D40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Bifurcations in context of PDEs (35B32) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)
Related Items (2)
Cites Work
- Unnamed Item
- Reaction-diffusion-advection models for the effects and evolution of dispersal
- On a chemotaxis model with saturated chemotactic flux
- The existence and stability of nontrivial steady states for S-K-T competition model with cross diffusion
- Qualitative analysis of a Lotka-Volterra competition system with advection
- Stationary and time-periodic patterns of two-predator and one-prey systems with prey-taxis
- Nonconstant positive steady states and pattern formation of 1D prey-taxis systems
- Chemotactic collapse for the Keller-Segel model
- Nonlinear scalar field equations. I: Existence of a ground state
- Pattern formation in competition-diffusion systems in nonconvex domains
- Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
- Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge
- Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
- A user's guide to PDE models for chemotaxis
- Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
- On global bifurcation for quasilinear elliptic systems on bounded domains
- Global stability in generalized Lotka-Volterra diffusion systems
- Point-condensation for a reaction-diffusion system
- Spatial segregation in competitive interaction-diffusion equations
- Geometric theory of semilinear parabolic equations
- Stationary pattern of some density-dependent diffusion system with competitive dynamics
- Effect of domain-shape on coexistence problems in a competition-diffusion system
- Existence of non-constant stable equilibria in competition-diffusion equations
- Diffusion vs cross-diffusion: An elliptic approach
- Effects of spatial grouping on the functional response of predators
- Global analysis of the predator--prey system with Beddington-DeAngelis functional response.
- Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes
- The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime
- Diffusion, self-diffusion and cross-diffusion
- Dynamics of a nonautonomous predator--prey system with the Beddington-DeAngelis functional response
- Point condensation generated by a reaction-diffusion system in axially symmetric domains
- Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem
- Bifurcation, perturbation of simple eigenvalues, and linearized stability
- Stability of monotone solutions for the shadow Gierer-Meinhardt system with finite diffusivity
- On the multi-dimensional advective Lotka-Volterra competition systems
- Boundedness vs. blow-up in a chemotaxis system
- Some global results for nonlinear eigenvalue problems
- Bifurcation from simple eigenvalues
- Stationary Solutions of a Volume-Filling Chemotaxis Model with Logistic Growth and Their Stability
- Stability of Spiky Solutions in a Competition Model with Cross-Diffusion
- The Existence and Stability of Spike Equilibria in the One‐Dimensional Gray–Scott Model: The Low Feed‐Rate Regime
- Global Asymptotic Stability of Lotka–Volterra Diffusion Models with Continuous Time Delay
- LPBounds of solutions of reaction-diffusion equations
- Activators and Inhibitors in Pattern Formation
- Global well-posedness of advective Lotka–Volterra competition systems with nonlinear diffusion
- Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion
- The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
- On the dynamics of predator-prey models with the Beddington-DeAngelis functional response
This page was built for publication: Global well-posedness, pattern formation and spiky stationary solutions in a Beddington-DeAngelis competition system