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Dynamics of Oxygen-Plankton Model with Variable Zooplankton Search Rate in Deterministic and Fluctuating Environments

Author

Listed:
  • Sudeshna Mondal

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

  • Guruprasad Samanta

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

  • Manuel De la Sen

    (Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Bizkaia, Spain)

Abstract

It is estimated by scientists that 50–80% of the oxygen production on the planet comes from the oceans due to the photosynthetic activity of phytoplankton. Some of this production is consumed by both phytoplankton and zooplankton for cellular respiration. In this article, we have analyzed the dynamics of the oxygen-plankton model with a modified Holling type II functional response, based on the premise that zooplankton has a variable search rate, rather than constant, which is ecologically meaningful. The positivity and uniform boundedness of the studied system prove that the model is well-behaved. The feasibility conditions and stability criteria of each equilibrium point are discussed. Next, the occurrence of local bifurcations are exhibited taking each of the vital system parameters as a bifurcation parameter. Numerical simulations are illustrated to verify the analytical outcomes. Our findings show that (i) the system dynamics change abruptly for a low oxygen production rate, resulting in depletion of oxygen and plankton extinction; (ii) the proposed system has oscillatory behavior in an intermediate range of oxygen production rates; (iii) it always has a stable coexistence steady state for a high oxygen production rate, which is dissimilar to the outcome of the model of a coupled oxygen-plankton dynamics where zooplankton consumes phytoplankton with classical Holling type II functional response. Lastly, the effect of environmental stochasticity is studied numerically, corresponding to our proposed system.

Suggested Citation

  • Sudeshna Mondal & Guruprasad Samanta & Manuel De la Sen, 2022. "Dynamics of Oxygen-Plankton Model with Variable Zooplankton Search Rate in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(10), pages 1-24, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1641-:d:813325
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    References listed on IDEAS

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    1. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2020. "Delay induced nonlinear dynamics of oxygen-plankton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Mondal, Sudeshna & Samanta, Guruprasad, 2022. "Dynamics of a delayed toxin producing plankton model with variable search rate of zooplankton," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 166-191.
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