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
N1 - Funding Information:
The authors are grateful to the editor Prof. Stefan Schuster and the anonymous reviewers for their useful comments and suggestions, which help us to modify the manuscript. We are also thankful to Dr. Nitai Debnath, Amity University, for a fruitful discussion. Sudip Samanta's research work is supported by Erasmus Mundus postdoctoral fellowship (EMINTE) . The research of J. Chattopadhyay is partially supported by a DST-SERB project (Ref No. SERB/F/0412/2013-2014 ).
Publisher Copyright:
© 2014 Elsevier Ireland Ltd.
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
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U2 - 10.1016/j.biosystems.2014.11.003
DO - 10.1016/j.biosystems.2014.11.003
M3 - Article
C2 - 25448892
AN - SCOPUS:84910627643
SN - 0303-2647
VL - 127
SP - 28
EP - 41
JO - BioSystems
JF - BioSystems
ER -