Applied Mathematics

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Applied Mathematics

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Browsing Applied Mathematics by Author "Ndebele-Murisa, M.R."

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    Bifurcation Analysis of a 5D Nutrient, Plankton, Limnothrissa miodon Model with Hydrocynus vittatus Predation
    (Journal of Applied Mathematics, 2022-07-20) Mutasa, F.K.; Jones, B.; Tendaupenyu, I.H.; Nhiwatiwa, T.; Ndebele-Murisa, M.R.
    In this paper, we construct and analyze a theoretical, deterministic 5D mathematical model of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus predation. Local stability analysis results agree with the numerical simulations in that the coexistence equilibrium is locally stable provided that certain conditions are satisfied. The coexistence equilibrium is globally stable if certain conditions are met. Existence, stability, and direction of Hopf bifurcations are derived for some parameters. Bifurcation analysis shows that the model undergoes Hopf bifurcation at the coexistence point for the zooplankton growth rate with periodic doubling leading to chaos.
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    Stability Analysis and Optimal Control of a Limnothrissa Miodon Model with Harvesting
    (Discrete Dynamics in Nature and Society, 2022-05-05) Mutasa, F.K.; Jones, B.; Hove-Musekwa, S.D.; Tendaupenyu, I.H.; Nhiwatiwa, T.; Ndebele-Murisa, M.R.
    We construct a theoretical, deterministic mathematical model of the dynamics of Limnothrissa miodon with nutrients, phytoplankton, and zooplankton and investigate the effect of harvesting on the population density of Limnothrissa miodon in a lake. For the autonomous model, results from local stability analysis are in agreement with numerical simulations in that the coexistence equilibrium is locally stable, provided certain conditions are satisfied. The coexistence equilibrium is globally unstable if it is feasible. Numerical results show that a stable limit cycle exists for the nonautonomous model. Optimal control results show an optimal harvesting monthly effort of 15394 boat nights which corresponds to 505 fishing units, showing that there is overcapacity in Lake Kariba. A maximum sustainable annual catch of 34669 tonnes is obtained and simulation results show that Limnothrissa miodon abundance is more closely related to nutrient inflow than to harvesting.