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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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Undamped oscillations in fractional-order Duffing oscillator
Signal Processing, 2015This paper studies undamped oscillations of fractional-order Duffing system. Stability theorems for fractional order systems are used to determine the characteristic polynomial of the system in order to find the parametric ranges for undamped oscillations in this system.
Mohammad Rostami, Mohammad Haeri
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Antiperiodic oscillations in a forced Duffing oscillator
Chaos, Solitons & Fractals, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
SHAW, PK +4 more
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Journal of Applied Nonlinear Dynamics, 2017
Summary: We present our investigation on the effect of parametric force on the response amplitude in the single Duffing oscillator and unidirectionally coupled \(n\) Duffing oscillators. In the single oscillator parametric perturbation is of the form \(f x \sin \omega t\).
Rajamani, S., Rajasekar, S.
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Summary: We present our investigation on the effect of parametric force on the response amplitude in the single Duffing oscillator and unidirectionally coupled \(n\) Duffing oscillators. In the single oscillator parametric perturbation is of the form \(f x \sin \omega t\).
Rajamani, S., Rajasekar, S.
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Behavior Evolution of Duffing Oscillator
2015 7th International Conference on Intelligent Human-Machine Systems and Cybernetics, 2015In this paper, the methods of random Melnikov process function are introduced to educe out the threshold of chaotic movement of non-linear system. We found that the non-Gaussian color noise effect on the chaos character of Duffing oscillator is decided by the value of parameters in the model, the non-Gaussian color noise has little effect on the system'
Yonghe Chen +3 more
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1994
The Duffing oscillator is one of the prototype systems of nonlinear dynamics. It first became popular for studying anharmonic oscillations and, later, chaotic nonlinear dynamics in the wake of early studies by the engineer Georg Duffing [8.1]. The system has been successfully used to model a variety of physical processes such as stiffening springs ...
H. J. Korsch, H.-J. Jodl
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The Duffing oscillator is one of the prototype systems of nonlinear dynamics. It first became popular for studying anharmonic oscillations and, later, chaotic nonlinear dynamics in the wake of early studies by the engineer Georg Duffing [8.1]. The system has been successfully used to model a variety of physical processes such as stiffening springs ...
H. J. Korsch, H.-J. Jodl
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Controlling the uncertain Duffing oscillator
1997 1st International Conference, Control of Oscillations and Chaos Proceedings (Cat. No.97TH8329), 2002In this paper, an adaptive feedback controller is developed based on the Lyapunov stability theory for an uncertain chaotic Duffing oscillator where only an approximate range of the three key system parameters are known. The proposed method can be extended to handle some other uncertain chaotic dynamical systems with mild modifications.
X. Dong, G. Chen, L. Chen
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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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Second Harmonics Effects in Random Duffing Oscillators
SIAM Journal on Applied Mathematics, 2005We consider a stochastic model for Duffing oscillators, where the nonlinearity and the randomness are scaled in such a way that they interact strongly. A typical feature is the appearance of second harmonics effects. An asymptotic statistical analysis for these oscillators is performed in the diffusion limit, when a suitable absorbing boundary ...
ACEBRON J. A, SPIGLER, Renato
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Coalescence in Coupled Duffing Oscillators
Chinese Physics Letters, 2009The forced Duffing oscillator has a pair of symmetrical attractors in a proper parameter regime. When a lot of Duffing oscillators are coupled linearly, the system tends to form clusters in which the neighboring oscillators fall onto the same attractor. When the coupling strength is strong, all of the oscillators fall onto one attractor.
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