Dynamic analysis of nonlinear variable frequency water supply system with time delay

Abstract

In this paper, we study the mathematical model about variable frequency water supply system in the process of applying glue to particleboard. Based on the original linear ordinary differential model, the effects of time delay and the nonlinear factor are considered. Then, we obtain the delayed nonlinear differential equation associated with variable frequency water supply system. Further, we consider the existence and stability of the equilibria and the existence of several types of bifurcations in this functional differential equation. Next, we derive the normal forms of Hopf bifurcation and Bogdanov–Takens bifurcation by using the multiple time scales method and the center manifold reduction method, respectively, and analyze the classifications of local dynamics. Finally, by using Matlab software, we obtain numerical simulations with estimated values of parameters and show the existence of stable equilibrium, stable periodic-1, periodic-2, and periodic-4 solutions, and a complex chaotic attractor from a sequence of period-doubling bifurcations.