A nonlinear dynamical model for oxygen depletion and fish mortality due to water hyacinth infestation

Abstract

Water hyacinth (Eichhornia crassipes) is a highly invasive aquatic plant that severely degrades freshwater ecosystems by depleting dissolved oxygen, disrupting nutrient dynamics, and threatening fish populations. In this study, we develop and analyze a dimensionless nonlinear dynamical model describing the interactions among water hyacinth biomass, nutrient concentrations (nitrogen and phosphorus), dissolved oxygen, and fish population. The model incorporates hyacinth growth, nutrient uptake, oxygen depletion, and oxygen-dependent fish dynamics. Through non-dimensionalization, the system is simplified, enabling a generalized analytical treatment. The existence, uniqueness, and boundedness of solutions are established to ensure biological feasibility. Equilibrium points are identified and analyzed for stability using center manifold theory and the Routh–Hurwitz criterion. Numerical simulations demonstrate threshold behavior governed by the fish reproduction to hyacinth growth ratio R, revealing that excessive hyacinth biomass leads to oxygen depletion and fish extinction, while higher R values stabilize the system and promote coexistence.