Journal ArticleDOI
The bifurcations of duffing's equation: An application of catastrophe theory
Peter J. Holmes,David A. Rand +1 more
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In this paper, the existence and stability of solutions of Dufng's equation are investigated and their characteristic bifurcations are studied, and it is shown how catastrophe theory provides a natural synthesis between the practical and theoretical aspects of the problem.About:
This article is published in Journal of Sound and Vibration.The article was published on 1976-01-22. It has received 146 citations till now. The article focuses on the topics: Catastrophe theory & Differential (mathematics).read more
Citations
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Journal ArticleDOI
A nonlinear oscillator with a strange attractor
TL;DR: In this paper, the authors studied the bifurcational behavior of a nonlinear oscillator with a qualitative viewpoint and showed that for a wide range of moderate f extremely complicated nonperiodic motions arise.
Journal ArticleDOI
Vortex-induced vibrations of a long flexible circular cylinder
D. Brika,A. Laneville +1 more
TL;DR: In this article, an experimental study of the vortex-induced oscillations of a long flexible circular cylinder was performed and the observed stationary amplitudes describe an hysteresis loop partially different from earlier studies.
Book ChapterDOI
Chaotic Phenomena Triggering the Escape from a Potential Well
TL;DR: In this paper, the authors explore the manner in which a driven mechanical oscillator escapes from the cubic potential well typical of a metastable system close to a fold, and show how the well-known atoms of dissipative dynamics (saddle-node folds, period-doubling flips, cascades to chaos, boundary crises, etc.) assemble to form molecules of overall response.
Journal ArticleDOI
Data based identification and prediction of nonlinear and complex dynamical systems
TL;DR: The recent advances in this forefront and rapidly evolving field of reconstructing nonlinear and complex dynamical systems from measured data or time series are reviewed, aiming to cover topics such as compressive sensing, noised-induced dynamical mapping, perturbations, reverse engineering, synchronization, inner composition alignment, global silencing and Granger Causality.
Journal ArticleDOI
Superstructure in the bifurcation set of the Duffing equation ẍ + dẋ + x + x3 = f cos(ωt)
Ulrich Parlitz,Werner Lauterborn +1 more
TL;DR: In this article, a periodic recurrence of a specific fine structure in the bifurcation set, which is closely connected with the nonlinear resonances of the system, is investigated.
References
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Vibration problems in engineering
TL;DR: In this article, the Probleme dynamique and Vibration were used for propagation of ondes reference records created on 2004-09-07, modified on 2016-08-08.
Book ChapterDOI
Differentiable dynamical systems
TL;DR: A survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M is presented in this paper.
Book
Differential Equations, Dynamical Systems, and Linear Algebra
Morris W. Hirsch,Steve Smale +1 more
TL;DR: In this article, the structure theory of linear operators on finite-dimensional vector spaces has been studied and a self-contained treatment of that subject is given, along with a discussion of the relations between dynamical systems and certain fields outside pure mathematics.
Book
Vibration Theory and Applications
TL;DR: Vibration theory and applications as mentioned in this paper, VIBT and applications, VIBR theory and application, Vibration Theory and Applications, Vibrration theory, and applications.