Coexistence of two strongly competitive species in a reaction–advection–diffusion system

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 a combination of 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 results are obtained by analyzing the stability of semitrivial solutions. 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, particularly for relatively moderate interspecific competition parameters in species with directional movement. These findings underscore the crucial role of directed movement and interspecific competition coefficients in shaping the dynamics and coexistence of strongly competing species.