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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Impact of Refuge Prey: A bottom-up top-down Phytoplankton-Zooplankton Interaction Model

Journal of Applied Nonlinear Dynamics 11(1) (2022) 179--194 | DOI:10.5890/JAND.2022.03.011

Anal Chatterjee$^1$, Samares Pal$^2$

$^1$ Department of Mathematics, Barrackpore Rastraguru Surendranath College, North 24 Parganas 700120, India

$^2$ Department of Mathematics, University of Kalyani, Kalyani- 741235, India

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Abstract

A detailed study on the effect of refuge on the phytoplankton-zooplankton ecosystem is explored. At first, the coexistence and stability conditions of different equilibria of the plankton system are analyzed. Our observations established that refuges have a strong impact on plankton dynamics. When the strength of phytoplankton crosses a certain critical value, the coexistence equilibrium loses its stability and enters into Hopf bifurcation that leads to oscillations of all species. The direction of the Hopf bifurcation is also established. Next, we used Pontryagins maximum principle to study a path of optimal harvesting policy. Also, we observed that the bottom-up and top-down effects like constant nutrient input, rate of zooplankton decay due to the toxic effect of phytoplankton play important roles for switching from one steady state to another that relates to the transcritical bifurcation. We derived the bifurcation scenarios when two different parameters vary together at the same time. At last, numerical simulations are implemented to support our results.

Acknowledgments

The research of Samares Pal is partially supported by Science and Engineering Research Board, Government of India, Grant No. CRG/2019/003248.

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