Dynamic analysis and control in a differential-algebraic harmful phytoplankton blooms model

A harvested allelopathic two-species phytoplankton ecosystem is investigated by a differential-algebraic model. By using the differential-algebraic system theory and bifurcation theory, local stability of the proposed model around the interior equilibrium is studied. Furthermore, instability mechanism of the proposed model due to variation of economic interest of harvesting is discussed. With the purpose of stabilizing the proposed model around the interior equilibrium and maintaining the economic interest of harvesting at an ideal level, state feedback controllers are designed. Finally, numerical simulations are carried out to show the effectiveness of designed controllers.