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Structure in the bifurcation diagram of the Duffing oscillator
Physical Review E, 1995We identify four levels of structure in the bifurcation diagram of the two-well periodically driven Duffing oscillator, plotted as a function of increasing control parameter T, the period of the driving term. The superstructure, or bifurcation peninsula, repeats periodically as T increases by \ensuremath{\sim}2\ensuremath{\pi}, beginning and ending ...
, Gilmore, , McCallum
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Adaptive Control of the Uncertain Duffing Oscillator
International Journal of Bifurcation and Chaos, 1997An adaptive feedback controller is developed based on rigorous Lyapunov argument for an uncertain chaotic Duffing oscillator, in which the three key system parameters are essentially unknown. The proposed method can be easily extended to handle some other chaotic dynamical systems with mild modifications.
Dong, Xiaoning +2 more
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VIBRATIONAL RESONANCE IN AN ASYMMETRIC DUFFING OSCILLATOR
International Journal of Bifurcation and Chaos, 2011We analyze how the asymmetry of the potential well of the Duffing oscillator affects the vibrational resonance. We obtain, numerically and theoretically, the values of the low-frequency and amplitude of the high-frequency forces at which vibrational resonance occurs.
S. Jeyakumari +3 more
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The Duffing oscillator with damping
European Journal of Physics, 2015Summary: An analytical solution to the differential equation describing the Duffing oscillator with damping is presented. The damping term of the differential equation and the initial conditions satisfy an algebraic equation, and thus the solution is specific for this type of damping.
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Analysis and synthesis of perturbed Duffing oscillators
International Journal of Circuit Theory and Applications, 2006AbstractAnalysis and synthesis of perturbed Duffing oscillators have been presented. The oscillations in such systems are regarded as limit cycles in perturbed Hamiltonian systems under polynomial perturbations of sixth degree and are analysed by using the Melnikov function.
V. Savov, Zhivko Georgiev, Todor Todorov
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ON THE CROSS WAVELET ANALYSIS OF DUFFING OSCILLATOR
Journal of Sound and Vibration, 1999228
Kyprianou, Andreas +3 more
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Time Optimal Control and the Duffing Oscillator
IMA Journal of Applied Mathematics, 1972This paper is an introduction to time optimal control problems for second order systems, while the example of the Duffing oscillator is used to illustrate the difficulties introduced by multiple solutions of the Maximum Principle. The phenomenon of lobesweeping is described and both swept and unswept switching curves given in the strongly nonlinear ...
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Duffing oscillators: Control and memory effects
Physical Review E, 2008In the first part of this article we study the hysteretic bistable response of Duffing oscillators and show ways to control the switching between stable branches of this nonlinear response. The control mechanism is either applied through a pulse that can be in phase or out of phase with the periodic driving force or through a frequency-modulated ...
Adriano A, Batista +2 more
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Capture into resonance of coupled Duffing oscillators
Physical Review E, 2015In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations ...
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The saddle case of Rayleigh–Duffing oscillators
Nonlinear Dynamics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Hebai, Huang, Deqing, Jian, Yupei
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