Double Hopf bifurcation in active control system with delayed feedback: application to glue dosing processes for particleboard

In this paper, we study dynamics in delayed active control system, with particular attention focused on double Hopf bifurcation. Firstly, we identify the critical values for stability switches, Hopf and double Hopf bifurcations using the method of bifurcation analysis. Secondly, by applying the multiple time scales method, the normal form near the double Hopf bifurcation, as well as classifications of local dynamics is analyzed. Finally, an example, associated with active control of ball valve in glue dosing processes for particleboard, is presented to demonstrate the application of the theoretical results. Numerical simulations, including stable equilibrium, stable periodic solutions and stable quasiperiodic solutions, are presented.