Results 181 to 190 of about 7,979 (231)

Quasiperiodic solutions of Duffing’s equations

Nonlinear Analysis: Theory, Methods & Applications, 1998
The existence of quasiperiodic solutions and the boundedness of all solutions to the equation \[ {d^2x \over dt^2}+ x^{2n+1} +\sum^l_{k=0} x^kp_k(t)=0,\;l\leq 2n, \] where \(p_0,\dots,p_l\) are quasi-periodic functions with frequencies \(\omega_1,\dots,\omega_m\), are considered. The Diophantine condition \(|k_1\omega_1+ \cdots+ k_m\omega_m|\geq c/ |k|^
Liu, Bin, You, Jiangong
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Integrable Duffing’s maps and solutions of the Duffing equation

Chaos, Solitons & Fractals, 2003
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Murakami, Wakako, Murakami, Chieko, Hirose, Kei-ichi, Ichikawa, Yoshi H.   +3 more
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Bifurcations and Chaos in Duffing Equation

Acta Mathematicae Applicatae Sinica, English Series, 2007
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Zhang, Meng, Yang, Jiangping
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FRACTIONAL DUFFING'S EQUATION AND GEOMETRICAL RESONANCE

International Journal of Bifurcation and Chaos, 2013
We investigate the Fractional Duffing equation in the presence of nonharmonic external perturbations. We have applied the concept of Geometrical Resonance to this equation. We have obtained the conditions that should be satisfied by the external driving forces in order to produce high-amplitude periodic oscillations avoiding chaos.
Jiménez, S., González, J. A., Vázquez, L.   +2 more
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2π-Periodic solutions of Duffing's equation

USSR Computational Mathematics and Mathematical Physics, 1986
The common properties of different classes of \(2\pi\)-periodic solutions of Duffing's nonlinear differential equation are investigated analytically and numerically. Generating periodic solutions are examined. The basic properties of \(2\pi\)-periodic solutions are investigated using the nonlinear functional analysis method.
Galaktionova, O. O., Zlatoustov, V. A.
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Periodic solutions for Duffing equations

Nonlinear Analysis: Theory, Methods & Applications, 1995
The main result proved by the authors in this paper states that if \(k\) is the minimal positive integer such that \((k- 1)^2< A< k^2< B< \infty\), and there exists \(\beta\in C[0, 2\pi]\) such that \(A\leq f_y(x, y)\leq \beta(x)\leq B\) and \(\int^{2\pi}_0 \beta(x) dx< 2\pi A+ 2(B- A)\alpha_k\), where \(\alpha_k\) is the minimal positive root of the ...
Wang, H., Li, Y.
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Periodic Solutions of Discontinuous Duffing Equations

Qualitative Theory of Dynamical Systems, 2020
The author considers a scalar differential equation of the type \[ x''+g(x)=e(t), \] where \(e:{\mathbb R}\to {\mathbb R}\) is continuous and \(T\)-periodic, and \(g:{\mathbb R}\to {\mathbb R}\) has a discontinuity at the origin, with \(\lim_{x\to0^\pm}g(x)\in {\mathbb R}\) but different.
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An Alternative Analysis of Duffing’s Equation

SIAM Review, 1992
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Parametric Frequency Analysis of Mathieu–Duffing Equation

International Journal of Bifurcation and Chaos, 2021
The classic linear Mathieu equation is one of the archetypical differential equations which has been studied frequently by employing different analytical and numerical methods. The Mathieu equation with cubic nonlinear term, also known as Mathieu–Duffing equation, is one of the many extensions of the classic Mathieu equation. Nonlinear characteristics
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Experimental mimicry of Duffing's equation

Journal of Sound and Vibration, 1992
Abstract Extensive analytical and numerical investigations have focused on Duffing's equation. However, experimental work, in a mechanics context, has been limited to studying systems the stiffness characteristics of which can be approximated by a non-linear (cubic) restoring force; e.g., a buckled beam excited transversely or a rigid pendulum ...
J.A. Gottwald, L.N. Virgin, E.H. Dowell
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