Parametrics Resonances of a Forced Modified Rayleigh-Duffing Oscillator

We investigate in this paper the superharmonic and subharmonic resonances of forced modified Rayleigh-Duffing oscillator. We analyse this equation by the method of multiple scales and we obtain superharmonic, subharmonic resonances order-two and order-three and primary resonance. We obtain also regions where steady-state subharmonic responses exist. We also use the amplitude-frequency curve for demonstrate the effect of various parameters on the response of the system. Finally, we focus our attention on chaotic motion of this oscillator by simulation. We obtain that this oscillator is chaotic for certains values for natural and excitation frequency but chaotic motion is not the same in subharmonic and superharmonic cases.