Stability and Bifurcations in a Nutrient–Phytoplankton–Zooplankton Model with Delayed Nutrient Recycling with Gamma Distribution

Two nutrient–phytoplankton–zooplankton (NZP) models for a closed ecosystem that incorporates delay in nutrient recycling, obtained using the gamma distribution function with one or two degrees of freedom, are analysed. The described by systems ordinary differential equations four and five dimensions. purpose this study is to investigate how mean total nutrients affect stability equilibrium solutions. Local theory bifurcation used determine long-time dynamics models. It found both exhibit comparable qualitative dynamics. There maximum three points each models, at most them locally asymptotically stable. change from another takes place through transcritical bifurcation. In some hypotheses on functional response, loses via supercritical Hopf bifurcation, causing apparition stable limit cycle. way which results consistent prior research they extend discussed. Finally, various application-related consequences theoretical deduced.