The modelling and control of a singular biological economic system with a species migration and environment damage

The paper deals with singular biological economic model of species population and environment at permanent area, meanwhile presenting stage structure. Firstly, the ecosystem of the area is represented by a set of nonlinear differential equations involving migration and environment. Then, we analyze the local stability of equilibriums of the system when the economic profit parameter is zero. By applying the singular systems theory and bifurcation theory, it is shown that the conditions of the singularity induced bifurcation under the positive equilibrium. In order to eliminate the singularity induced bifurcation, we design a state-feedback controller by controlling the strength of environmental protection. At last, We are numerically simulating to support the results of the analysis.