On Self-Excited Auto-Parametric Systems

We consider a Rayleigh type of self-excited auto-parametricsystem. We study the semi-trivial solution and its domain of instabilitywhere non-trivial solutions are initiated. We are interested in theexistence and stability of the non-trivial solutions and we analyze thebehaviour of the solutions by examining it for various values of someparameters. We divide the discussion on the non-trivial solution inexact resonance and near resonance cases. In the analysis we use bothnormal forms (or averaging) and numerical bifurcation path-followingtechniques. The system displays a rich pattern of differentbifurcations, a robust heteroclinic cycle and instability behaviour.