Global Dynamics of a Duffing System with Delayed Velocity Feedback
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The paper presents the rich dynamics of a damped Duffing oscillator with negative feedback of delayed velocity. When the absolute value of feedback gain is less than the damping coefficient, the equilibrium of system is delay-independent stable. Otherwise, it undergoes a number of stability switches with an increase of time delay, and becomes unstable at last. At each stability switch, a Hopf bifurcation occurs. The amplitude and frequency of the bifurcated periodic motion depend on the time delay. When the time delay is long enough, any perturbed motion from the unstable equilibrium may become chaotic though the oscillator of single degree of freedom is autonomous. All these features come from the infinite dimensions of system owing the time delay. They explain why a flexible structure under negative velocity feedback exhibits various self-excited vibrations when the feedback gain is large.
Key wordsDelay control stability switch Hopf bifurcation basin of attraction
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- A.H. Nayfeh, C.M. Chin, and J. Pratt, “Perturbation methods in nonlinear dynamics: applications to machining dynamics,” Journal of Manufacture Science and Technology 119: 485–493, 1997.Google Scholar