Impact of Nanomaterial in the Marine Environment: Through Mathematical Modelling by Eco-Path Framework

Authors

  • Kalyan Das Department of Interdisciplinary Sciences, National Institute of Food Technology Entrepreneurship and Management, Kundli, Haryana 131028, India
  • M.N. Srinivas Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India 3Department of Mathematics, Aliah University, Kolkata 700156, India
  • Aktar Saikh Department of Mathematics, Aliah University, Kolkata 700156, India
  • Md. Haider Ali Biswas Mathematics Dicipline, Khulna University, Khulna 9208, Bangladesh

DOI:

https://doi.org/10.5614/cbms.2024.7.1.8

Keywords:

Phytoplankton zooplankton, nanoparticles, mathematical model, functional responses, stability analysis, bifurcation

Abstract

We propose and analyze a simple modification to the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model to account for the interference of the predators with the impacts of nanoparticles. We have taken into account the influence of predators by quantifying the impact of nanoparticles in actual environments. It is shown that the influence of the nanoparticles may reduce the prey's maximum physiological per-capita growth rate. An elementary Lotka-Volterra uptake term is taken into consideration in order to investigate the nanoparticle dynamics or interactions. Most importantly, our research shows that phytoplankton growth suppression caused by nanoparticles can destabilize the system and cause periodic oscillation. Additionally, it was demonstrated that a decrease in the equilibrium densities of both phytoplankton and zooplankton might occur from an increase in the rate of interaction between the nanoparticles and phytoplankton. Additionally, the study shows that the stable coexistence of the system dynamics depends critically on the aquatic system's nanoparticles being depleted. We also looked into the system using different kinds of functional reactions. Compared to other commonly used ecology, The complex relationship that exists between phytoplankton and nanoparticles in the natural environment is better described by the Monod-Haldane functional response.

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Published

2024-10-01

How to Cite

Das, K., Srinivas, M., Saikh, A. ., & Biswas, M. H. A. (2024). Impact of Nanomaterial in the Marine Environment: Through Mathematical Modelling by Eco-Path Framework. Communication in Biomathematical Sciences, 7(1), 148-161. https://doi.org/10.5614/cbms.2024.7.1.8

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