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Modelling and analysis of Limnothrissa miodon population in a Lake

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  • Mutasa, Farikayi K.
  • Jones, Brian
  • Musekwa-Hove, Senelani D.

Abstract

A mathematical model of nutrients, phytoplankton, zooplankton and Limnothrissa miodon is formulated, analysed and simulated. The model is analyzed to gain insight into the qualitative features of the equilibrium states, which enable us to determine their stability. We employ analytical and numerical techniques to investigate the impact of nutrients and intra-specific competition on the population density of Limnothrissa miodon. Stability analysis results agree with the simulations in that the coexistence equilibrium is locally asymptotically stable provided certain conditions are met. The coexistence equilibrium is globally-asymptotically stable if a certain condition is met. The inflow rate of the nutrients has a positive effect on the coexistence equilibrium, whereas the Limnothrissa miodon intra-specific competition, has a negative effect on the coexistence equilibrium. Theoretical and numerical simulations show that the nutrients inflow rate is key to the productivity of the water body and that the population of Limnothrissa miodon will continue to thrive in the water body as long as the nutrient inflow rate, is greater than some threshold value.

Suggested Citation

  • Mutasa, Farikayi K. & Jones, Brian & Musekwa-Hove, Senelani D., 2020. "Modelling and analysis of Limnothrissa miodon population in a Lake," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302447
    DOI: 10.1016/j.chaos.2020.109844
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    References listed on IDEAS

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    1. Beibei Wang & Min Zhao & Chuanjun Dai & Hengguo Yu & Nan Wang & Pengfei Wang, 2016. "Dynamics Analysis of a Nutrient-Plankton Model with a Time Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-12, January.
    2. S. Kartal & M. Kar & N. Kartal & F. Gurcan, 2016. "Modelling and analysis of a phytoplankton–zooplankton system with continuous and discrete time," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 22(6), pages 539-554, November.
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