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Experimental chaos detection in the Duffing oscillator
Communications in Nonlinear Science and Numerical Simulation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-Sire Armand Eyébé Fouda +3 more
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Oscillations near a separatrix in the duffing equation
Proceedings of the Steklov Institute of Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Duffing Oscillator with Damping for a Softening Potential
International Journal of Applied and Computational Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Secure communication using Duffing oscillators
2011 IEEE International Conference on Signal and Image Processing Applications (ICSIPA), 2011In this paper, a Duffing oscillator is used to construct a chaos-based secure communication system for transmitting digital signals. The synchronization of both the transmitter and the receiver is carried out using a Lyapunov-based control approach that observes the states of the transmitter.
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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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On the Third Superharmonic Resonance in the Duffing Oscillator
Journal of Sound and Vibration, 1994Abstract The third order superharmonic resonance in two versions of a harmonically excited Duffing oscillator is investigated by analytical and numerical methods. It is shown that even in situations for which a non-linear oscillator may be thought a priori to satisfy the "small perturbation" requirements, the analytical results obtained by the ...
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Regular and irregular motions in a duffing oscillator
International Applied Mechanics, 2000The author studies the Duffing equation \(\frac{dx^2}{d\xi^2} + h \frac{dx}{d\xi} - x(\kappa - \gamma x^2) = f(\Omega\xi)\) under periodic external excitation with frequency \(\Omega\). A relationship is established between the symmetry of quasistatic solutions and regularity of motions occurring due to the periodic perturbation.
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Resonance and Symmetry Breaking for a Duffing Oscillator
SIAM Journal on Applied Mathematics, 1989Summary: The solution of ẍ\(+2\delta \dot x+x(1-x^ 2)=\epsilon \sin \omega t\) is approximated by \(x=a_ 0+a_ 1\sin \omega t\), and \(a_ 1=a_ 1(\omega;\delta,\epsilon)\) is determined on the hypothesis that \(a_ 0=0\). It is shown that this symmetric solution is stable, except on that segment of the resonance curve \((a_ 1 vs \omega)\) that connects ...
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2013
Numerical integration of the non-stationary Schrödinger equation with Duffing potential depending on two coordinates has been carried out. Oscillation types and the influence of coupling between two oscillators on frequency spectra are analyzed in detail.
Sanin, A., Semyonov, E.
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Numerical integration of the non-stationary Schrödinger equation with Duffing potential depending on two coordinates has been carried out. Oscillation types and the influence of coupling between two oscillators on frequency spectra are analyzed in detail.
Sanin, A., Semyonov, E.
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