# Fuzzy Control for a class of Singular Bio-Economic System

【摘要】：This paper establishes a singular bio-economic model with "prey-predator-top predator", discusses the stability and the bifurcation and eliminates the bifurcation by using the method of fuzzy control. Firstly, according to the "prey-predatortop predator" behavior phenomenon, a singular bio-economic model is built and the necessary and sufficient conditions for the stability of the equilibrium point of singular bio-economic model are given. Secondly, by applying the singular systems theory and bifurcation theory, it is shown that the sufficient conditions of the singularity induced bifurcation under the positive equilibrium. As the same time, in order to eliminate the singularity induced bifurcation, a state-feedback controller by fuzzy control method is designed. At last, we apply our results to a practical example.

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