# Active Control of the Parametric Resonance in the Modified Rayleigh-Duffing Oscillator

@article{Miwadinou2013ActiveCO, title={Active Control of the Parametric Resonance in the Modified Rayleigh-Duffing Oscillator}, author={Cl{\'e}ment Hod{\'e}v{\`e}wan Miwadinou and A. V. Monwanou and J. B. Chabi Orou}, journal={arXiv: Fluid Dynamics}, year={2013} }

The present paper examines the active control of parametric resonance in modified Rayleigh-Duffing oscillator. We used the method of averaging to obtain steady-state solutions. We have found the critical value of the parametrical amplitude which indicates the boundary layer where the control is efficient in reducing the amplitude vibration. We have also found the effects of excitation parameters and time-delay on dynamical of this system with the principal parametric resonance. We have obtained…

## 7 Citations

Melnikov Chaos in a Modified Rayleigh-Duffing Oscillator with ϕ6 Potential

- Computer Science, MathematicsInt. J. Bifurc. Chaos
- 2016

The chaotic behavior of the modified Rayleigh–Duffing oscillator with ϕ6 potential and external excitation is investigated both analytically and numerically and it is pointed out that certain quadratic damping effects are contrary to cubic damping effect.

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

- Mathematics, Computer ScienceInt. J. Bifurc. Chaos
- 2015

The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos in the case of the Modified Rayleigh-Duffing Oscillator and it is found the effects of unpure quadratic parameter and amplitude of parametric excitation on the critical Melnikov amplitude $\mu_{cr}$.

Hysteresis, Quasiperiodicity and Chaoticity in a Nonlinear Dissipative Hybrid Oscillator

- Physics
- 2017

Hysteresis, quasi-periodicity and chaoticity in a nonlinear dissipative hybrid oscillator are studied. The modified Rayleigh-Duffing oscillator is considered. We simultaneously take into account the…

Effect of nonlinear dissipation on the basin boundaries of a driven two-well or catastrophic single-well Modified Rayleigh-Duffing Oscillator

- Mathematics
- 2013

This paper considers effect of nonlinear dissipation on the basin boundaries of a diven two-well Modified Rayleigh-Duffing Oscillator where pure and unpure quadratic and cubic nonlinearities are…

Nonlinear dynamics of a $$\varvec{\phi ^6}-$$ϕ6- modified Duffing oscillator: resonant oscillations and transition to chaos

- Physics
- 2017

The nonlinear dynamics of a hybrid Rayleigh–Van der Pol–Duffing oscillator includes pure and impure quadratic damping are investigated. The multiple timescales method is used to study exhaustively…

Modeling nonlinear dissipative chemical dynamics by a forced modified Van der Pol-Duffing oscillator with asymmetric potential: Chaotic behaviors predictions

- Physics
- 2018

Abstract This paper addresses the issues of nonlinear chemical dynamics modeled by a modified Van der Pol-Duffing oscillator with asymmetric potential. The Melnikov method is utilized to analytically…

Nonlinear dynamics of system oscillations modeled by a forced Van der Pol generalized oscillator

- Mathematics, Physics
- 2014

This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $…

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