Dynamical behavior in a differential-algebraic algal blooms model

In this paper, we consider a differential-algebraic model which links the outbreak and biological control strategy of algal blooms. In the proposed mathematical model, two interacting algal species are investigated by a two-species Lotka-Volterra competition differential model, and an algebraic equation is presented to study the economic interest of harvest effort on some algal. The occurrence mechanism of algal blooms is revealed by analyzing the local stability of the proposed model system at the interior equilibrium. Furthermore, the instability mechanism of the proposed model system due to the variation of economic interest of harvesting is studied. With the purpose of eliminating the algal blooms and maintaining the economic interest of harvesting at an ideal level, a biological control strategy corresponding to a state feedback controller in the proposed model system is designed. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis obtained in this paper.