On the Delayed van der Pol Oscillator with Time-Varying Feedback Gain

Mustapha Hamdi; Mohamed Belhaq

doi:10.4028/www.scientific.net/AMM.706.149

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 706On the Delayed van der Pol Oscillator with...

On the Delayed van der Pol Oscillator with Time-Varying Feedback Gain

Abstract:

This work studies the effect of time delayed feedback on stationary solutions in a van derPol type system. We consider the case where the feedback gain is harmonically modulated with a resonantfrequency. Perturbation analysis is conducted to obtain the modulation equations near primaryresonance, the stability analysis for stationary solutions is performed and bifurcation diagram is determined.It is shown that the modulated feedback gain position can influence significantly the steadystates behavior of the delayed van der Pol oscillator. In particular, for appropriate values of the modulateddelay parameters, the existence region of the limit cycle (LC) can be increased or quenched.Moreover, new regions of quasiperiodic vibration may emerge for certain values of the modulatedgain. Numerical simulation was conducted to validate the analytical predictions.

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Periodical:

Applied Mechanics and Materials (Volume 706)

Pages:

149-158

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.706.149

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Online since:

December 2014

Authors:

Mustapha Hamdi*, Mohamed Belhaq

Keywords:

Control, Limit Cycle, Time Delay, Time-Periodic Feedback Gain, Van Der Pol Oscillator

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* - Corresponding Author

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