Singularity-induced bifurcation and control for a class of bioeconomic system

Abstract

Differential-algebraic bioeconomic systems are a new research field in differential-algebraic systems; there has been little research about bifurcations and fuzzy control of differential-algebraic bioeconomic systems. Bifurcations analysis and feedback controller design of the system offers an important basis for the research of differential-algebraic system theory applied to bioeconomic systems. In this paper, the problems of singularity-induced bifurcation (SIB), impulsive behavior and corresponding control for a class of differential-algebraic bioeconomic systems are discussed. Firstly, by the theory of differential-algebraic systems, it is obtained that there exist the SIB and impulsive behavior in the system. Secondly, Takagi-Sugeno (T-S) fuzzy descriptor models are constructed. Then, a feedback controller is designed to make the system to be stable. As a result, the SIB and impulsive behavior can be eliminated by the control method of T-S fuzzy descriptor systems. In practice, it can be realized by controlling the harvesting effort. Finally, numerical simulations illustrate that the controller is effective.