Interplay of resource mappings and evolutionary diffusion: Competitive exclusion and coexistence analysis

Abstract

We study a directed dynamical reaction–diffusion model with no-flux boundary conditions where two populations interact in a spatial heterogeneous closed environment state. Both populations growths are proportional to the same growth law, but the dispersal policies with the migration coefficients differ. The population is diffusing according to their resource functions, and the carrying capacity is bounded in a heterogeneous habitat. This paper’s main results are: if the dispersion functions are non-proportional, then the coexistence is not possible unless the whole environment is homogeneous; and in case of proportionality, the species shows similar behavior. The coexistence is possible if the resource phase and the distribution function of a second organism are identical and non-constant. A few numerical examples verify that the extinction of one species by the other and the coexistence are visible in a non-homogeneous environment.

Keywords

• Competition
• Directed diffusion
• Global stability
• Resource distributions
• Numerical solutions