Self-excited auto-parametric systems

Abstract

We consider a Rayleigh type of selfexcited autoparametric system We study the semitrivial solution and its domain of instability where nontrivial solutions are initiated We are interested in the existence and stability of the nontrivial solutions and we analyze the behaviour of the solutions by examining it for various values of some parameters We divide the discussion on the nontrivial solution in exact resonance and near resonance cases In the analysis we use both normal forms or averaging and numerical bifurcation pathfollowing techniques The system displays a rich pattern of dierent bifurcations a robust heteroclinic cycle and instability behaviour