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

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