Parametrics Resonances of a Forced Modified Rayleigh-Duffing Oscillator

TL;DR

This paper analyzes the resonance behaviors and chaotic motion of a forced modified Rayleigh-Duffing oscillator using multiple scales, revealing how system parameters influence steady-state responses and chaos onset.

Contribution

It introduces a detailed analysis of superharmonic, subharmonic, and primary resonances in the oscillator, including the effects of parameters on responses and chaos, using analytical and simulation methods.

Findings

Identification of superharmonic, subharmonic, and primary resonances.

Regions where steady-state subharmonic responses occur.

Chaotic motion depends on natural and excitation frequencies.

Abstract

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.