Parametrics Resonances of a Forced Modified Rayleigh-Duffing Oscillator

Abstract

We investigate in this paper the superharmonic and subharmonic resonances of forced modified Rayleigh-Duffing oscillator. We analyse this equation by 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 and we obtain that this oscillator is chaotic for certains values for natural and excitation frequency but chaotic motion it is not the same in subharmonic and superharmonic cases.

Effect of Nonlinear Dissipation on the Basin Boundaries of a Driven Two-Well Modified Rayleigh–Duffing Oscillator

“…This oscillator is used to modelize the following phenomenon: a El Niño Southern Oscillation (EN SO) coupled tropical ocean-atmosphere weather phenomenon in which the state variables are temperature and depth of a region of the ocean called the thermocline (where the annual seasonal cycle is the parametric excitation and the model exhibits a Hopf bifurcation in the absence of parametric excitation), a M EM S device consisting of a 30µm diameter silicon disk which can be made to vibrate by heating it with a laser beam resulting in a Hopf bifurcation (where the parametric excitation is provided by making the laser beam intensity vary periodically in time) etc. [16] and [18].…”