Abstract: Considering the economic theory of public fishery， a preypredator bioeconomic model with time delay was studied. It was showed that transcritical bifurcation， singular induced bifurcation and saddlenode bifurcation would occur with no time delay. Under the condition of zero harvesting， prey and predator would be coexisted. With time delay， there existed two positive equilibrium points. Hopf bifurcation and small amplitude periodic solutions would occur， which caused switching of stability. The state feedback controller eliminated bifurcation phenomenon. By using Matlab software， the effectiveness of mathematical conclusions were verified by some numerical simulations.

Key words: differentialalgebraic bioeconomic model, transcritical bifurcation, singular induced bifurcation, saddlenode bifurcation, Hopf bifurcation