Bifurcations in an autoparametric system in 1:1 internal resonance with parametric excitation

Abstract

We consider an autoparametric system which consists of an oscillator coupled with a parametricallyexcited subsystem The oscil lator and the subsystem are in internal resonance The excited subsystem is in parametric resonance with the external forcing The system contains the most general type of cubic nonlinearities Us ing the method of averaging and numerical bifurcation continuation we study the dynamics of this system In particular we consider the sta bility of the semitrivial solutions where the oscillator is at rest and the excited subsystem performs a periodic motion We nd various types of bifurcations leading to nontrivial periodic or quasiperiodic solu tions We also nd numerically sequences of perioddoublings leading to chaotic solutions