Bifurcation Analysis of a 5D Nutrient, Plankton, Limnothrissa miodon Model with Hydrocynus vittatus Predation - Farikayi K. Mutasa; Brian Jones; Itai H. Tendaupenyu; Tamuka Nhiwatiwa; Mzime R. Ndebele-Murisa (Journal of Applied Mathematics)
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.