In this paper, we improve a new mathematical model associated with glue flow control system for glue applying of particleboard. Firstly, we study the existence and stability of the equilibria and the existence of fold, Hopf and Bogdanov-Takens bifurcations in above system. Next, the normal forms of Hopf bifurcation and Bogdanov-Takens bifurcation are derived, and the classifications of local dynamics near above bifurcation critical values are analyzed. Then, numerical simulation results show that the flow control system associated with glue applying of particleborad exists stable equilibrium, stable periodic-1, periodic-2, and periodic-4 solutions, and chaotic attractor phenomenon from a sequence of period-doubling bifurcations. Finally, we compare the dynamical phenomena of flow control system with and without cubic terms, showing that cubic terms can effect the dynamical behaviors of flow control system.