Effects of anisotropic diffusion in a two-dimensional unstirred chemostat

We investigate an unstirred chemostat model in which two species compete in a two-dimensional environment. The populations are assumed to disperse anisotropically, with distinct probabilities assigned to horizontal and vertical movements, which are interpreted as dispersal strategies. First, we analyze the dynamics of the single-species model and identify the conditions for the existence of positive steady states. Then, we classify the dynamical behavior of the two-species model into three scenarios based on the diffusion strategies: (i) extinction; (ii) competitive exclusion; and (iii) coexistence. Next, we provide sufficient conditions for the existence of coexistence steady states. Finally, our numerical simulations provide visual validation of our theoretical results and offer valuable insights for future researches.