The effect of nanoparticles on plankton dynamics: A mathematical model

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


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
Publication statusPublished - Jan 1 2015


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • General Biochemistry,Genetics and Molecular Biology
  • Applied Mathematics


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