Stability and Hopf Bifurcation Analysis of a Phytoplankton-Zooplankton Model Under Temperature Factor and Stage-Structure Population of Phytoplankton

Abstract

In the paper, we built a predator-prey model to simulate and study the dynamics of zooplankton and phytoplankton populations under the temperature impact, in which the stage structure is considered in the zooplankton population. Our model is an ordinary differential system of three nonlinear equations with some parameters as temperature-dependent functions and uses the generalized Holling response function. The non-negative and boundedness of the model solutions have been proven. The behaviors of our system are shown by the local stability conditions of the equilibria, especially the co-existence case. The stage transformation of zooplankton was studied through the Hopf bifurcation results of varying the temperature. The analysis and simulation results indicate that the ideal temperature for the co-existence is about 12-21 degrees Celsius. The zooplankton's transformation decreases when the temperature increases, leading to an imbalance in the system. Besides that, we also provided simulation figures to illustrate the found theoretical results.