Weak Competition Case Research Articles

Global dynamics of a competition model with nonlocal dispersal II: The full system

In this paper, we study logistic models with non-local dispersal for two competing species. In the weak competition case, the global asymptotic behavior of solutions is completely classified provided one of the following conditions is valid:•one diffusion rate is small;•one diffusion rate is large;•two diffusion rates are close. This is a continuation of the work [16]. Our results illustrate the effects of non-local dispersals and interspecific competition coefficients in the competition system with spatially heterogeneous environments.

Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions

A Lotka-Volterra competition model with nonlinear boundary conditions is considered. First, by using upper and lower solutions method for nonlinear boundary problems, we investigate the existence of positive solutions in weak competition case. Next, we prove that-d1Δu=u(a1-b1u-c1v),x∈Ω;-d2Δv=v(a2-b2u-c2v),x∈Ω;∂u/∂ν+f(u)=0,x∈∂Ω;∂v/∂ν+g(v)=0,x∈∂Ω, has no positive solution when one of the diffusion coefficients is sufficiently large.

Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems

In this paper we study the interactions between diffusion and heterogeneity of the environment in the classical diffusive Lotka--Volterra competition systems. In the weak competition case, we establish the uniqueness, hence the global asymptotic stability, of coexistence steady states under various circumstances, and thereby we obtain a complete understanding of the change in dynamics when one of the interspecific competition coefficients is small.

Uniform boundedness and convergence of solutions to the systems with a single nonzero cross-diffusion

Uniform boundedness and convergence of global solutions are proved for quasilinear parabolic systems with a single nonzero cross-diffusion in population dynamics. Gagliardo–Nirenberg type inequalities are used in the estimates of solutions in order to establish W 1 2-bounds uniform in time. By using the uniform bound, convergence of solutions are established for systems with large diffusion coefficients in the weak competition case.