On the complex dynamic behaviour in nonlinear systems with delay

Oscillatory dynamic behaviour emerging from Hopf bifurcation phenomenon in nonlinear feedback systems with delay is presented. The periodic branches are recovered after using Harmonic Balance Approximations (HBA) and the theory of feedback control systems. The results are plotted and compared against those obtained by simulations. Furthermore, other static, dynamic and degenerate bifurcations are pointed out using this methodology in the so-called frequency domain. Two examples for illustrating the application of this technique are included.