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The generalized Duffing oscillator
Communications in Nonlinear Science and Numerical Simulation, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nikolai A Kudryashov
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On the dynamics of the Rayleigh–Duffing oscillator
Nonlinear Analysis: Real World Applications, 2019Consider the planar system \[ \frac{dx}{dt}= y,\quad \frac{dy}{dt}=-ax-2bxy-x^3-y^3. \] The authors prove that this system \begin{itemize} \item[(i)] has no global analytic first integrals, \item[(ii)] has no Darboux polynomials, \item[(iii)] is not Darboux integrable, \item[(iv)] is not Liouville integrable, \item[(v)] does not have any center neither
Jaume Gine, Claudia Valls
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Thermodynamics of Duffing’s Oscillator
Journal of Applied Mechanics, 1994We study the averaged characteristics of the response of Duffing’s oscillator to harmonic excitation. We show that, as in classical thermodynamics, response characteristics are potential functions of excitation characteristics.
Berdichevsky, V., Özbek, O., Kim, W. W.
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A GEOMETRIC MODEL FOR THE DUFFING OSCILLATOR
International Journal of Bifurcation and Chaos, 1993A geometric model for the Duffing oscillator is constructed by analyzing the unstable periodic orbits underlying the chaotic attractors present at particular parameter values. A template is constructed from observations of the motion of the chaotic attractor in a Poincaré section as the section is swept for one full period.
McCallum, J. W. L., Gilmore, R.
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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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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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The nonstationary effects on a softening duffing oscillator
Mechanics Research Communications, 1994Object of the numerical investigations is the equation \(\ddot x(t)+ x(t)+ 0,4\dot x (t)- x^3 (t)= f(t)\cos \theta (t)\) with \(\dot \theta(t)= \Omega (t)\). First, the stationary case \((f=\text{const}\), \(\Omega= \text{const})\) is considered and a bifurcation diagram along the \(\Omega\)-line \((\Omega (t)= \Omega_0+ \alpha t)\) is obtained.
Lu, C. H., Evan-Iwanowski, R. M.
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Numerical study on synchronization in the Rayleigh–Duffing and Duffing oscillators
International Journal of Modern Physics C, 2023A study on the master-slave synchronization scheme between Rayleigh–Duffing and Duffing oscillators is presented. We analyze the elastic and dissipative couplings and a combination of both. We compare the results to explore which coupling is more effective to achieve synchronization between both oscillators.
U. Uriostegui-Legorreta, E. S. Tututi
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Duffing oscillators for secure communication
Computers & Electrical Engineering, 2018Abstract This paper introduces a new technique for using chaotic Duffing oscillators in secure communication. The secret message is encrypted using the parameters of the Duffing oscillator that indirectly affect the generated chaotic orbits. The mathematical model of the chaotic transmitter uses three parameters that can be altered between two levels,
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