Effect of polluted environment on one prey and two competing predators with Gompertz growth and Beddington-DeAngelis functional response

Freshwater ecosystems are increasingly threatened by pollutants that disrupt species interactions and ecosystem stability. This study develops and analyzes a nonlinear eco-toxicological mathematical model that couples phytoplankton, two competing zooplankton species, and an environmental toxicant. The phytoplankton growth is modeled using a Gompertz function to capture stress-driven asymmetry, while predator–prey interactions follow a Beddington–DeAngelis functional response. Toxicant input, decay, and phytoplankton uptake are incorporated into the mathematical system. We establish positivity, boundedness, and the existence of five biologically feasible equilibria, followed by a detailed stability analysis using Jacobian eigenvalues and Routh–Hurwitz criteria. Sensitivity indices show that parameters linked to the zooplankton (predator) populations have the strongest influence on equilibrium levels, while toxicant-related parameters govern the stability transitions. Numerical simulations confirm the stability of non-trivial equilibria and reveal that increases in toxicant input rate and phytoplankton mortality due to toxicity can trigger subcritical Hopf bifurcations, leading to oscillatory instabilities. The results underscore the ecological importance of toxicant thresholds in freshwater communities and provide insight into how pollution influences coexistence, resilience, and the risk of ecosystem destabilization.