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.
authors.affiliation: Department of Statistics, Visva-Bharati University, Santiniketan, West Bengal 731235, India.
authors.forename: Sourav
authors.initials: S
authors.lastname: Rana
authors.affiliation: Department of Biomathematics and Game Theory, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland.
authors.forename: Sudip
authors.initials: S
authors.lastname: Samanta
authors.affiliation: Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India.
authors.forename: Sabyasachi
authors.initials: S
authors.lastname: Bhattacharya
authors.affiliation: Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India.
authors.forename: Kamel
authors.initials: K
authors.lastname: Al-Khaled
authors.affiliation: Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India.
authors.forename: Arunava
authors.initials: A
authors.lastname: Goswami
authors.affiliation: Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Oman. Electronic address: joydev@isical.ac.in.
authors.forename: Joydev
authors.initials: J
authors.lastname: Chattopadhyay
mesh_terms: D000818:Animals; D003198:Computer Simulation; D020387:Food Chain; D008954:Models, Biological; D053758:Nanoparticles / Q000633:toxicity*; D010839:Phytoplankton / Q000187:drug effects / Q000254:growth & development*; D011157:Population Dynamics; D015048:Zooplankton / Q000254:growth & development*
keywords: Bifurcation; Functional responses; Mathematical model; Nanoparticles; Phytoplankton; Stability analysis; Zooplankton