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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.Abstract:
Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.read more
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A review of the recent research on vibration energy harvesting via bistable systems
Ryan L. Harne,Kon-Well Wang +1 more
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Past, present and future of nonlinear system identification in structural dynamics
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A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
TL;DR: A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002) as mentioned in this paper.
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On the Concept of Attractor
TL;DR: In this article, a definition for the concept of "attractor" was proposed based on the probable asymptotic behavior of orbits, and the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor.