Title: Role of constant nutrient input and mortality rate of plankton population in marine plankton ecosystem

Authors: Anal Chatterjee; Samares Pal

Addresses: Department of Mathematics, Sheikhpara A.R.M. Polytechnic, Murshidabad, Sheikhpara 742409, West Bengal, India ' Department of Mathematics, University of Kalyani, Kalyani 741235, West Bengal, India

Abstract: In this paper, we have proposed a plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved limiting nutrient with type II functional response and instantaneous nutrient recycling. The model system is studied analytically and the threshold conditions for the existence and stability of various steady states are worked out. It is shown that the positive equilibrium loses its stability if the constant nutrient input crosses a certain critical value and the system enters into Hopf bifurcation that induces oscillations of the populations. Our observations indicate that mortality rate of plankton population plays an important role to change steady state to oscillatory behaviour of the system. We derive the bifurcation scenarios when both the parameters constant nutrient input and mortality rate of plankton vary together. It is interesting to observe that the additional food source for zooplankton population plays a vital role to change the steady state behaviour. The results are illustrated by numerical simulations.

Keywords: additional food; algal bloom; Hopf bifurcation; constant nutrient input; mortality rate; plankton population; marine plankton ecosystems; phytoplankton; zooplankton; nutrient recycling; population oscillations; oscillatory behaviour; numerical simulation.

DOI: 10.1504/IJDSDE.2016.079028

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.3, pp.234 - 253

Received: 17 Jun 2015
Accepted: 03 Feb 2016
Published online: 09 Sep 2016 *

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