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All Journal Jambura Journal of Biomathematics (JJBM)
Makwana, Kavita
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Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

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Modeling the Impact of Toxicants on a Plankton-Fish System with Gompertz Growth Function Annavarapu, Raveendra Babu; Makwana, Kavita; Jadon, Bhanu Pratap Singh
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 2: June 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i2.30824

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.
Effect of Toxicant on One Prey and Two Competing Predators with Beddington-DeAngelis Functional Response Makwana, Kavita; A., Raveendra Babu; Jadon, B.P.S.
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 1: March 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i1.30686

Abstract

This study investigates the dynamical behaviour of a prey-predator system with two competing predators, incorporating the Beddington–DeAngelis functional response and the effects of environmental toxicants. Analytical analysis ensures the boundedness of solutions, guaranteeing biologically feasible population dynamics. Equilibrium points are identified, and their stability is examined using local and global stability analyses. Numerical simulations validate the analytical findings, demonstrating that as the competition coefficient b1 increases, the system transitions from a stable equilibrium to periodic oscillations and eventually to chaotic behaviour. Furthermore, the impact of the toxicant uptake rate d1 is explored to assess its role in system stability. The results indicate that low levels of toxicant absorption promote oscillatory dynamics, while higher values of d1 suppress population growth and restore stability. This highlights the dual role of toxicants in ecological systems, where moderate exposure disrupts equilibrium, but excessive accumulation can lead to stabilization. Bifurcation diagrams and time-series simulations further reinforce these transitions, revealing critical thresholds where stability is lost or regained. The study provides valuable insights into the complex interplay between toxicant dynamics, predator-prey interactions, and bifurcation phenomena. The findings emphasize the ecological implications of toxicant exposure and interspecies competition, offering potential applications in environmental management and conservation strategies.
Co-Authors A., Raveendra Babu Annavarapu, Raveendra Babu Jadon, B.P.S. Jadon, Bhanu Pratap Singh