Results 231 to 240 of about 8,845 (277)

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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On controllability of Duffing equation

Applied Mathematics and Computation, 2013
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Loi, Nguyen Van, Obukhovskii, Valeri
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The generalized duffing equation with large damping

International Journal of Non-Linear Mechanics, 1968
Abstract The equation x + 2p x + ω 2 0 x + μ n x = 0 where n is an odd integer greater than or equal to 3, x(0) = A0, and x (0) = 0 has received much attention in the literature but always with the restrictions that μ and p are small.
Ludeke, C. A., Wagner, W. S.
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On Quasi-periodic Perturbations of Duffing Equation

The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2016
Summary: Quasi-periodic two-frequency perturbations are studied in a system which is close to a nonlinear two-dimensional Hamiltonian one. The example of Duffing equation with a saddle and two separatix loops is considered. Several problems are studied: dynamical behavior in a neighborhood of a resonance level of the unperturbed system, conditions for ...
Morozov, A. D., Dragunov, T. N.
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Duffing equation and action functional

Nonlinear Analysis: Theory, Methods & Applications, 2011
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Boundedness of solutions for semilinear duffing equations

Applied Mathematics and Computation, 2002
The author studies the boundedness of all solutions of the equation \(x''+n^{2}x+f(x) = p(t)\). The main result is the following theorem: Suppose \(f(x) \in C^{\infty } ({\mathbb R}), p(t)\in C^{6} ({\mathbb R}/2 \pi {\mathbb Z})\). If \(\int^{2\pi }_{0} p(t)e^{-int}dt = 0\) and if \(f(x)\) satisfies the following conditions: the limits \(\lim \limits_{
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