The effects of diffusion and spatial variation in Lotka–Volterra competition–diffusion system I: Heterogeneity vs. homogeneity

Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity

“…Especially, for the case of heterogeneity vs. homogeneity with equal amount of total resources and b = 1, c = 1, He and Ni [14,17] obtained thoroughly complete global dynamics of (1.2). More precisely, in [14,17], He and Ni proposed the…”

“…Recently, by allowing the species U and V to have different intrinsic growth rates or to different distributions of resources, in a series of works, He and Ni [14][15][16][17] studied the following Lotka-Volterra model of competition-diffusion system:…”

“…Our main concern in this paper is to pursue the dynamics system (1.3), especially the affect of advection rate α, β on the dynamics of this system. When α = β = 0, system (1.3) becomes the system (1.2), which is studied by He and Ni [14][15][16][17] recently. By detailed computation and analysis, He and Ni [14][15][16][17] obtained some dramatic picture of global dynamics of (1.2) based on diffusion rates d 1 and d 2 .…”

“…When α = β = 0, system (1.3) becomes the system (1.2), which is studied by He and Ni [14][15][16][17] recently. By detailed computation and analysis, He and Ni [14][15][16][17] obtained some dramatic picture of global dynamics of (1.2) based on diffusion rates d 1 and d 2 . Especially, for the case of heterogeneity vs. homogeneity with equal amount of total resources and b = 1, c = 1, He and Ni [14,17] obtained thoroughly complete global dynamics of (1.2).…”

“…The following notations of subsets of the first quadrant of the d 1 d 2 -plane for (1.4) is also used in [14,17]: For the precise definition of linear stability/instability of a steady state and their characterization, see e.g., [3]. We refer the readers to the beginning of Section 2 where the concept is defined via the sign of appropriate principal eigenvalues.…”