Advective Models with Nonlinear Boundary Conditions for Aquatic Population Persistence in Polluted River Ecosystems

• Xiaowei Qu ^[1] ; Shangjiang Guo ^[1]
  1. [1] China University of Geosciences

     China University of Geosciences

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • To investigate the long-term dynamics of population-toxicant interactions in polluted river systems with capture and purification mechanisms, we develop a novel reactiondiffusion-advection model incorporating complex nonlinear Danckwerts boundary conditions at the downstream end, generalising classical homogeneous boundary treatments. Using monotone dynamical systems theory, we demonstrate that the competitive system with these nonlinear boundary conditions generates a strongly monotone dynamical system, enabling complete characterisation of global dynamics. Through spectral analysis of associated eigenvalue problems, we establish the existence and stability criteria for both exclusion and coexistence steady states, and obtain sufficient conditions for population extinction versus toxicant coexistence. Our analytical results reveal that population persistence is critically influenced by two factors: the river’s advection velocity, and the toxicant’s effect coefficient. The theoretical framework developed here provides rigorous mathematical foundations for predicting ecological outcomes in polluted flowing environments with anthropogenic interventions.

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