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Dynamical Analysis of Phytoplankton–Zooplankton Interaction Model by Using Deterministic and Stochastic Approach

In: Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells

Author

Listed:
  • Anal Chatterjee

    (Barrackpore Rastraguru Surendranath College, Department of Mathematics)

  • Samares Pal

    (University of Kalyani, Department of Mathematics)

Abstract

In this chapter, we have considered a nutrient–phytoplankton–zooplankton interaction model in which phytoplankton is assumed to be able to detect the presence of zooplankton and to counteract it by forming patches and releasing some toxic chemicals in the surrounding water. Our observations indicate that the degree of toxicity plays an important role in changing one steady state to other steady state and oscillatory behavior of the system. It is observed that the control procedure proposed in the deterministic case holds strong even in environmental disturbances when the intensity of environmental fluctuations is maintained under the specific threshold value. We derive the bifurcation scenarios when not only a single parameter varies but also two different parameters vary together at the same time. The results are illustrated by numerical simulations.

Suggested Citation

  • Anal Chatterjee & Samares Pal, 2021. "Dynamical Analysis of Phytoplankton–Zooplankton Interaction Model by Using Deterministic and Stochastic Approach," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, pages 33-56, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-73241-7_3
    DOI: 10.1007/978-3-030-73241-7_3
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