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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

Dynamics of a Plankton-Fish Model with Infection in Phytoplankton Species

Journal of Applied Nonlinear Dynamics 12(4) (2023) 689--706 | DOI:10.5890/JAND.2023.12.005

Prabir Panja

Department of Applied Science and Humanities, Haldia Institute of Technology, Haldia, West Bengal, India

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Abstract

In this article, we formulate a predator-prey interaction model among phytoplankton, zooplankton and fish species. It is assume that phytoplankton species is infected by a disease and due to infection, phytoplankton population is divide into two subpopulation such as susceptible phytoplankton and infected phytoplankton. It is consider that zooplankton consume susceptible as well as infected phytoplankton and fish consume only zooplankton. Here, it is assume that the plankton population releases some toxin which make some death of zooplankton. We also study the existence of Hopf bifurcation for the present model with respect to the disease infection rate. It is observe that increase rate of infection of phytoplankton may cause the extinction of zooplankton as well as fish species. It is find that the increase of rate of consumption of susceptible phytoplankton by zooplankton may make the system stable. The increase rate of release of toxin by phytoplankton may make the system unstable. The proposed system may continue stable steady state behaviour due to the increase of conversion rate of zooplankton in fish species. Chaotic dynamics is observe, due to the addition of diffusion term in the present model.

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