Variable Structure Control of Singular Biological Economic System with Restrictive Human Behavior

In this paper, a singular bio-economic system with stage structure and time delay is established to study the impact of human reducing activities on biological population density. The local stability and dynamic behavior of the proposed model are studied. In the case of economic equilibrium, the local stability of the system with time delay at the equilibrium point is considered. Because the instability of the system will lead to the imbalance of biological population density in a short time. The sliding surface is designed based on the reaching law, and the variable structure controller is designed to ensure the stability of the system. Finally, the validity of the conclusion is verified by numerical simulation. It can be found that restricting human activities can minimize the impact on population density.