Jambura Journal of Biomathematics (JJBM)
Volume 6, Issue 2: June 2025

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

Annavarapu, Raveendra Babu (Unknown)
Makwana, Kavita (Unknown)
Jadon, Bhanu Pratap Singh (Unknown)



Article Info

Publish Date
29 Jun 2025

Abstract

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.

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Journal Info

Abbrev

JJBM

Publisher

Subject

Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

Description

Jambura Journal of Biomathematics (JJBM) aims to become the leading journal in Southeast Asia in presenting original research articles and review papers about a mathematical approach to explain biological phenomena. JJBM will accept high-quality article utilizing mathematical analysis to gain ...