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Duffing's equation and nonlinear resonance
International Journal of Mathematical Education in Science and Technology, 2003The phenomenon of nonlinear resonance (sometimes called the ‘jump phenomenon’) is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto an ...
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Solution of the Duffing Equation
1994Consider the Duffing equation with variable excitation and constant coefficients α, β, γ $$\begin{gathered} {\text{u''}} + \alpha u' + \beta u + \gamma {u^3} = \delta (t) \hfill \\ u(0) = {c_0}{\text{ u'(0) = }}{{\text{c}}_1} \hfill \\ \end{gathered} % MathType!End!2!1! $$ δ(t) will be written as a series δ(t) = Σ n=0 ∞ δntn. Let L = d2/dt2. Then
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A General Solution of the Duffing Equation
Nonlinear Dynamics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Almost periodic solutions for nonlinear duffing equations
Acta Mathematica Sinica, 1997Consider the Duffing differential equation \[ d^2x/dt^2- x+ x^3= f(t),\tag{\(*\)} \] where \(f\) is almost periodic. By using the theory of exponential dichotomy, the author first proves that \((*)\) has a unique bounded solution provided \(|f|\leq 8/27\).
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Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller
Journal of Low Frequency Noise Vibration and Active Control, 2022Chun-Hui He, Dan Tian, Marwa H Zekry
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The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation
Numerical Methods for Partial Differential Equations, 2021Ji-Huan He, Yusry O El-Dib
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