Stability analysis of nonlinear glue flow system with delay

Abstract

In this paper, we improve a new mathematical model associated with glue applying of particleboard. First, we study the existence and stability of the equilibria and the existence of fold, Hopf, and Bogdanov–Takens bifurcations in above system. Second, 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 glue flow system associated with glue applying of particleboard 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 glue flow system with frequency water supply system, showing that cubic terms which the latter lacks, could influence the dynamical behaviors of glue flow system.