The effect of nanoparticles on plankton dynamics: A mathematical model

Sourav Rana, Sudip Samanta, Sabyasachi Bhattacharya, Kamel Al-Khaled, Arunava Goswami, Joydev Chattopadhyay

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A simple modification of the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model with the interference of the predators by adding the effect of nanoparticles is proposed and analyzed. It is assumed that the effect of these particles has a potential to reduce the maximum physiological per-capita growth rate of the prey. The dynamics of nanoparticles is assumed to follow a simple Lotka-Volterra uptake term. Our study suggests that nanoparticle induce growth suppression of phytoplankton population can destabilize the system which leads to limit cycle oscillation. We also observe that if the contact rate of nanoparticles and phytoplankton increases, then the equilibrium densities of phytoplankton as well as zooplankton decrease. Furthermore, we observe that the depletion/removal of nanoparticles from the aquatic system plays a crucial role for the stable coexistence of both populations. Our investigation with various types of functional response suggests that Beddington functional response is the most appropriate representation of the interaction of phytoplankton-nanoparticles in comparison to other widely used functional responses.

Original languageEnglish
Pages (from-to)28-41
Number of pages14
JournalBioSystems
Volume127
DOIs
Publication statusPublished - Jan 1 2015

Fingerprint

Plankton
Phytoplankton
Nanoparticles
Theoretical Models
Mathematical Model
Mathematical models
Functional Response
Zooplankton
Predator
Prey
Lotka-Volterra
Depletion
Growth
Coexistence
Limit Cycle
Population
Interference
Contact
Oscillation
Decrease

Keywords

  • Bifurcation
  • Functional responses
  • Mathematical model
  • Nanoparticles
  • Phytoplankton
  • Stability analysis
  • Zooplankton

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Rana, S., Samanta, S., Bhattacharya, S., Al-Khaled, K., Goswami, A., & Chattopadhyay, J. (2015). The effect of nanoparticles on plankton dynamics: A mathematical model. BioSystems, 127, 28-41. https://doi.org/10.1016/j.biosystems.2014.11.003

The effect of nanoparticles on plankton dynamics : A mathematical model. / Rana, Sourav; Samanta, Sudip; Bhattacharya, Sabyasachi; Al-Khaled, Kamel; Goswami, Arunava; Chattopadhyay, Joydev.

In: BioSystems, Vol. 127, 01.01.2015, p. 28-41.

Research output: Contribution to journalArticle

Rana, S, Samanta, S, Bhattacharya, S, Al-Khaled, K, Goswami, A & Chattopadhyay, J 2015, 'The effect of nanoparticles on plankton dynamics: A mathematical model', BioSystems, vol. 127, pp. 28-41. https://doi.org/10.1016/j.biosystems.2014.11.003
Rana S, Samanta S, Bhattacharya S, Al-Khaled K, Goswami A, Chattopadhyay J. The effect of nanoparticles on plankton dynamics: A mathematical model. BioSystems. 2015 Jan 1;127:28-41. https://doi.org/10.1016/j.biosystems.2014.11.003
Rana, Sourav ; Samanta, Sudip ; Bhattacharya, Sabyasachi ; Al-Khaled, Kamel ; Goswami, Arunava ; Chattopadhyay, Joydev. / The effect of nanoparticles on plankton dynamics : A mathematical model. In: BioSystems. 2015 ; Vol. 127. pp. 28-41.
@article{06cdf40fadc04df6987814fd41dce76a,
title = "The effect of nanoparticles on plankton dynamics: A mathematical model",
abstract = "A simple modification of the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model with the interference of the predators by adding the effect of nanoparticles is proposed and analyzed. It is assumed that the effect of these particles has a potential to reduce the maximum physiological per-capita growth rate of the prey. The dynamics of nanoparticles is assumed to follow a simple Lotka-Volterra uptake term. Our study suggests that nanoparticle induce growth suppression of phytoplankton population can destabilize the system which leads to limit cycle oscillation. We also observe that if the contact rate of nanoparticles and phytoplankton increases, then the equilibrium densities of phytoplankton as well as zooplankton decrease. Furthermore, we observe that the depletion/removal of nanoparticles from the aquatic system plays a crucial role for the stable coexistence of both populations. Our investigation with various types of functional response suggests that Beddington functional response is the most appropriate representation of the interaction of phytoplankton-nanoparticles in comparison to other widely used functional responses.",
keywords = "Bifurcation, Functional responses, Mathematical model, Nanoparticles, Phytoplankton, Stability analysis, Zooplankton",
author = "Sourav Rana and Sudip Samanta and Sabyasachi Bhattacharya and Kamel Al-Khaled and Arunava Goswami and Joydev Chattopadhyay",
year = "2015",
month = "1",
day = "1",
doi = "10.1016/j.biosystems.2014.11.003",
language = "English",
volume = "127",
pages = "28--41",
journal = "BioSystems",
issn = "0303-2647",
publisher = "Elsevier Ireland Ltd",

}

TY - JOUR

T1 - The effect of nanoparticles on plankton dynamics

T2 - A mathematical model

AU - Rana, Sourav

AU - Samanta, Sudip

AU - Bhattacharya, Sabyasachi

AU - Al-Khaled, Kamel

AU - Goswami, Arunava

AU - Chattopadhyay, Joydev

PY - 2015/1/1

Y1 - 2015/1/1

N2 - A simple modification of the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model with the interference of the predators by adding the effect of nanoparticles is proposed and analyzed. It is assumed that the effect of these particles has a potential to reduce the maximum physiological per-capita growth rate of the prey. The dynamics of nanoparticles is assumed to follow a simple Lotka-Volterra uptake term. Our study suggests that nanoparticle induce growth suppression of phytoplankton population can destabilize the system which leads to limit cycle oscillation. We also observe that if the contact rate of nanoparticles and phytoplankton increases, then the equilibrium densities of phytoplankton as well as zooplankton decrease. Furthermore, we observe that the depletion/removal of nanoparticles from the aquatic system plays a crucial role for the stable coexistence of both populations. Our investigation with various types of functional response suggests that Beddington functional response is the most appropriate representation of the interaction of phytoplankton-nanoparticles in comparison to other widely used functional responses.

AB - A simple modification of the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model with the interference of the predators by adding the effect of nanoparticles is proposed and analyzed. It is assumed that the effect of these particles has a potential to reduce the maximum physiological per-capita growth rate of the prey. The dynamics of nanoparticles is assumed to follow a simple Lotka-Volterra uptake term. Our study suggests that nanoparticle induce growth suppression of phytoplankton population can destabilize the system which leads to limit cycle oscillation. We also observe that if the contact rate of nanoparticles and phytoplankton increases, then the equilibrium densities of phytoplankton as well as zooplankton decrease. Furthermore, we observe that the depletion/removal of nanoparticles from the aquatic system plays a crucial role for the stable coexistence of both populations. Our investigation with various types of functional response suggests that Beddington functional response is the most appropriate representation of the interaction of phytoplankton-nanoparticles in comparison to other widely used functional responses.

KW - Bifurcation

KW - Functional responses

KW - Mathematical model

KW - Nanoparticles

KW - Phytoplankton

KW - Stability analysis

KW - Zooplankton

UR - http://www.scopus.com/inward/record.url?scp=84910627643&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84910627643&partnerID=8YFLogxK

U2 - 10.1016/j.biosystems.2014.11.003

DO - 10.1016/j.biosystems.2014.11.003

M3 - Article

AN - SCOPUS:84910627643

VL - 127

SP - 28

EP - 41

JO - BioSystems

JF - BioSystems

SN - 0303-2647

ER -