Stability analysis of forced duffing oscillator (FDO)

The Duffing oscillator is one of the prototypes of nonlinear dynamics. Jump phenomenon can be induced by either varying the amplitude or the frequency of excitation. A comprehensive study of jump phenomenon of the duffing oscillator in two parameters (amplitude and frequency of excitation) is performed here. The analysis is based on a method of multiple time scale(MMS). In this research the stability conditions as well as unstable regimes on the frequency response curve are determined. The research also focuses on the stability of the dynamic motion of FDO. The amplitude response displays hysteresis in the frequency domain and jump phenomenon is observed in the case of primary resonance of duffing oscillator. The response of a vander Pol oscillator with sinusoidally varying amplitude is also discussed for non linear resonance. Here a method is devised to control the amplitude of oscillations. Hence Multiple harmonics are obtained as well as spring behaviour is also controlled by tweaking the cubic term of forced duffing oscillator.