Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

Publications

2 Dynamical Analysis of a Harvesting Model of Phytoplankton-Zooplankton Interaction

Authors: Anuj K. Sharma, Amit Sharma, Kulbhushan Agnihotri

Abstract:

In this work, we propose and analyze a model of Phytoplankton-Zooplankton interaction with harvesting considering that some species are exploited commercially for food. Criteria for local stability, instability and global stability are derived and some threshold harvesting levels are explored to maintain the population at an appropriate equilibrium level even if the species are exploited continuously.Further,biological and bionomic equilibria of the system are obtained and an optimal harvesting policy is also analysed using the Pantryagin’s Maximum Principle.Finally analytical findings are also supported by some numerical simulations.

Keywords: global stability, Phytoplankton-Zooplankton, Bionomic Equilibrium, Pontrying-Maximum Principal

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1 Bifurcation Analysis of a Plankton Model with Discrete Delay

Authors: Anuj Kumar Sharma, Amit Sharma, Kulbhushan Agnihotri

Abstract:

In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.

Keywords: Time Delay, Hopf-bifurcation, normal form theory, Plankton, Center manifold theorem

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