Modeling the Impact of Toxicants on a Plankton-Fish System with Gompertz Growth Function

This study develops a mathematical model to investigate the dynamics of an aquatic ecosystem, incorporating key ecological features such as Gompertz growth, prey refuge, Holling Type II predation, and the Beddington-DeAngelis functional response. The primary objective is to analyze the effects of toxicant accumulation and population interactions on ecosystem stability. Analytical techniques, including the Jacobian matrix, Routh-Hurwitz criteria, and Lyapunov functions—are employed to examine equilibrium points, stability conditions, and bifurcation behavior. A Hopf bifurcation is observed when the carrying capacity exceeds a critical threshold, indicating a transition from stable to oscillatory behavior. Intraspecific competition among fish is found to dampen chaotic dynamics, thereby enhancing system stability. Numerical simulations confirm the theoretical findings and highlight that increased toxicant levels disrupt energy flow through the food chain, causing population decline. These results underscore the importance of ecological regulation in preserving ecosystem balance and mitigating the impact of environmental stressors.