| Abstract: |
| The main focus of this article is to investigate the behavior of two strongly competitive species in a spatially heterogeneous environment using a Lotka-Volterra-type reaction-advection-diffusion model. The model assumes that one species diffuses at a constant rate while the other species moves toward a more favorable environment through constant diffusion and directional movement. The study finds that no stable coexistence can be guaranteed when both species disperse randomly. In contrast, stable coexistence between the two species is possible when one of the species exhibits advection-diffusion. The study also reveals the existence of unstable coexistence imposed by bistability in a strongly competitive system, regardless of the diffusion type. The study concludes that the species moving toward a better environment has a competitive advantage, allowing them to survive even when their population density is initially low. Finally, the study identifies the unique globally asymptotically stable coexistence steady states of the system at high advection rates. |
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