A review on the dynamics of two species competitive ODE and parabolic systems

Population dynamics (general) (92D25) General spectral theory of ordinary differential operators (34L05) Initial-boundary value problems for second-order parabolic systems (35K51) Monotone flows as dynamical systems (37C65)

Cites Work

Spatial Ecology via Reaction‐Diffusion Equations
On the finite-dimensional dynamical systems with limited competition
Monotonicity and Global Dynamics of a Nonlocal Two-Species Phytoplankton Model
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems
Effects of diffusion and advection on the smallest eigenvalue of an elliptic operator and their applications
On the Evolution of Slow Dispersal in MultiSpecies Communities
Lotka--Volterra Competition Model on Graphs
GLOBAL DYNAMICS OF A POPULATION MODEL FROM RIVER ECOLOGY
Asymptotic Behavior of the Principal Eigenvalue of a Linear Second Order Elliptic Operator with Small/Large Diffusion Coefficient
Asymptotics of the principal eigenvalue for a linear time-periodic parabolic operator II: Small diffusion
Asymptotic Behavior of the Basic Reproduction Ratio for Periodic Reaction-Diffusion Systems
Global dynamics of a Lotka–Volterra competition patch model*
A Spatiotemporal Model for the Effects of Toxicants on Populations in a Polluted River
On a Competition-Diffusion-Advection System from River Ecology: Mathematical Analysis and Numerical Study
Global Dynamics of a Lotka--Volterra Competition-Diffusion System in Advective Heterogeneous Environments
Global dynamics of a Lotka–Volterra competitive system from river ecology: general boundary conditions
The Logic of Animal Conflict
On a Nonlocal Reaction-Diffusion Problem Arising from the Modeling of Phytoplankton Growth
Advection-mediated coexistence of competing species
The Effect of Dispersal Patterns on Stream Populations
Dynamical systems in population biology
Zur Theorie der partiellen Differentialgleichungen.
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Asymptotic behavior of the principal eigenvalue for cooperative elliptic systems and applications
Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources. II
Reaction-diffusion-advection models for the effects and evolution of dispersal
The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system. II: The general case
Evolutionary convergence to ideal free dispersal strategies and coexistence
On the principal eigenvalue of linear cooperating elliptic systems with small diffusion
Dynamics of a three species competition model
Existence and nonexistence of positive steady states in multi-species phytoplankton dynamics
Dynamics of a reaction-diffusion-advection model for two competing species
Evolutionarily stable and convergent stable strategies in reaction-diffusion models for conditional dispersal
Evolution of dispersal in open advective environments
Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment
On a Lotka-Volterra competition model: the effects of advection and spatial variation
On a Lotka-Volterra competition system: diffusion vs advection
Can spatial variation alone lead to selection for dispersal?
Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model
Coexistence and bistability of a competition model in open advective environments
The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system I: Heterogeneity vs. homogeneity
Advection-mediated competition in general environments
Effects of heterogeneity on spread and persistence in rivers
Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka-Volterra competition model
Pattern formation in competition-diffusion systems in nonconvex domains
Strong positivity in \(C(\bar\Omega)\) for elliptic systems
Are two-patch models sufficient? The evolution of dispersal and topology of river network modules
Movement toward better environments and the evolution of rapid diffusion
Evolution of conditional dispersal: a reaction-diffusion-advection model
Evolution of dispersal and the ideal free distribution
Limiting profiles of semilinear elliptic equations with large advection in population dynamics
The evolution of conditional dispersal strategies in spatially heterogeneous habitats
The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
The evolution of slow dispersal rates: a reaction diffusion model
Diffusion-induced extinction of a superior species in a competition system
Effect of domain-shape on coexistence problems in a competition-diffusion system
A remark on the global asymptotic stability of a dynamical system modeling two species competition
The evolution of dispersal rates in a heterogeneous time-periodic environment
Global dynamics of a Lotka-Volterra competition-diffusion-advection system in heterogeneous environments
Global dynamics of a two species competition model in open stream environments
Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources. III
Evolution of passive movement in advective environments: general boundary condition
On a Lotka-Volterra type competition model from river ecology
Global dynamics of a classical Lotka-Volterra competition-diffusion-advection system
Convergence in competition models with small diffusion coefficients
Classification of global dynamics of competition models with nonlocal dispersals. I: Symmetric kernels
Diffusion, self-diffusion and cross-diffusion
Does movement toward better environments always benefit a population?
Saddle-point behavior for monotone semiflows and reaction-diffusion models
Evolution of a semilinear parabolic system for migration and selection in population genetics
On the asymptotic behavior of the principal eigenvalues of some elliptic problems
Global dynamics of a Lotka-Volterra competition-diffusion system in advective homogeneous environments
Global dynamics of a competition model with non-local dispersal. I: The shadow system
Ecological and evolutionary dynamics in advective environments: critical domain size and boundary conditions
Dynamical behaviors of a classical Lotka-Volterra competition-diffusion-advection system
Competitive exclusion in a nonlocal reaction-diffusion-advection model of phytoplankton populations
Global dynamics of a general competitive reaction-diffusion-advection system in one dimensional environments
On a second order eigenvalue problem and its application
Persistence, competition, and evolution
Global stability of nonhomogeneous steady-state solution in a Lotka-Volterra competition-diffusion-advection model
On the effects of carrying capacity and intrinsic growth rate on single and multiple species in spatially heterogeneous environments
Evolution of dispersal in advective homogeneous environments
Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments
Asymptotic behavior of the principal eigenvalue for cooperative periodic-parabolic systems and applications
Coexistence and bistability of a competition model with mixed dispersal strategy
Three-patch models for the evolution of dispersal in advective environments: varying drift and network topology
Evolution of conditional dispersal: evolutionarily stable strategies in spatial models
Global dynamics of a competition model with nonlocal dispersal. II: The full system
On a Lotka-Volterra competition-diffusion-advection system: homogeneity vs heterogeneity
Global dynamics of the diffusive Lotka-Volterra competition model with stage structure
Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small
A functional approach towards eigenvalue problems associated with incompressible flow
Evolution of dispersal in advective homogeneous environment: the effect of boundary conditions
Spatial patterns and coexistence mechanisms in systems with unidirectional flow
Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena
On the effects of migration and spatial heterogeneity on single and multiple species
On Lotka-Volterra competitive parabolic systems: exclusion, coexistence and bistability
Ecological and evolutionary dynamics in periodic and advective habitats
A remark on the global dynamics of competitive systems on ordered Banach spaces
Global Dynamics of the Lotka-Volterra Competition-Diffusion System: Diffusion and Spatial Heterogeneity I
Limiting Profiles of Semilinear Elliptic Equations with Large Advection in Population Dynamics II
Dynamics of strongly competing systems with many species
Effects of large degenerate advection and boundary conditions on the principal eigenvalue and its eigenfunction of a linear second order elliptic operator
On several conjectures from evolution of dispersal
Evolution of dispersal in closed advective environments
Asymptotics of the Principal Eigenvalue for a Linear Time-Periodic Parabolic Operator I: Large Advection
Existence of Steady-State Solutions for a One-Predator–Two-Prey System
Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model
Reaction–diffusion models with large advection coefficients
On an abstract competition model and applications
Operator matrices and reaction-diffusion systems
Asymptotic behaviour of solutions of periodic competition diffusion system
Effects of Random Motility on Microbial Growth and Competition in a Flow Reactor
Uniqueness and nonuniqueness of coexistence states in the lotka‐volterra competition model
Positive solutions for a three-species competition system with diffusion—I. General existence results