ON OSCILLATION TYPES IN FORCED NONLINEAR OSCILLATORS CLOSE TO HARMONIC RESONANCE

The influence of a periodic forcing on a nonlinear second-order oscillator close to a Hopf bifurcation point is investigated. It is assumed that the forcing frequency is close to the frequency of the Hopf bifurcation and that the forcing amplitude is small. By means of integral averaging, the given system is reduced to an autonomous system, which is investigated thoroughly. Periodic as well as quasiperiodic oscillations are shown to occur. A complete description of the bifurcations in the system together with explicit expressions determining the bifurcation diagrams is given. The results are applied to a self-exciting oscillator, and the conclusions are in accordance with earlier investigations.