Dynamics of Reaction-Diffusion-Advection System and its Impact on River Ecology in the Presence of Spatial Heterogeneity I

TL;DR

This paper investigates a reaction-diffusion-advection model with harvesting to understand how spatial heterogeneity affects competition and coexistence of two species in river ecosystems, using theoretical and numerical methods.

Contribution

It provides a comprehensive analysis of stability and coexistence in a heterogeneous environment with unequal diffusion and advection rates, extending previous models.

Findings

Existence, uniqueness, and positivity of solutions established

Local stability of semi-trivial steady states demonstrated

Non-existence of coexistence steady state under certain conditions

Abstract

In this study, a spatially distributed reaction-diffusion-advection (RDA) model with harvesting is investigated to signify the outcome of a competition between two competing species in a heterogeneous environment. The study builds upon the concept presented in literature \cite{tisha2}, applying it to river ecology in the context of harvesting activities. We assume that despite of having distinct advection and diffusion rates, two species are competing for the same food supply. This paper's main objective is to study, using theoretical and numerical analysis, the global asymptotic stability and coexistence steady state based on different and unequal rates of diffusion and advection. We establish the result for existence, uniqueness and positivity of the solution. The local stability of two semi trivial steady states is demonstrated. Also, we examine the non-existence of coexistence steady state with the help of some non-trivial presumptions. Finally, we combine the local stability with the non-existence of coexistence to demonstrate the global stability using monotone dynamical systems.