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Nayfeh, C.

Chin, and J. Pratt, "Applications of perturbation methods to tool chatter dynamics," in Dynamics and Chaos in Manufacturing Processes, F. Moon, Ed. Hu and Z. Li, J. Ji, C. Hansen, and C. Tan, "The response of a Duffing-van der Pol oscillator under delayed feedback control," Journal of Sound and Vibration, vol.

Chatterjee, "Self-excited oscillation under nonlinear feedback with time-delay," Journal of Sound and Vibration, vol. Alhazza, A. Nayfeh, and M. Daqaq, "On utilizing delayed feedback for active-multimode vibration control of cantilever beams," Journal of Sound and Vibration, vol.

Wheeler's delayed-choice experiment

Johnson, Nonlinear differential equations with delay as models for vibrations in the machining of metals, Ph. Belhaq, "Self-excited vibration control for axially fast excited beam by a time delay state feedback," Chaos, Solitons andFractals, vol. Houghton, S. Tobias, E. Knobloch, and M. Jung and P.

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Hanggi, "Bistability and colored noise in nonequilibrium systems: theory versus precise numerics," Physical Review Letters, vol. However, users may print, download, or email articles for individual use. CC BY. Similar topics of scientific paper in Mathematics , author of scholarly article — Mustapha Hamdi, Mohamed Belhaq Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes.

The response of nonlinear controlled system under an external excitation via time delay state feedback.

Model Structure Selection: Determining Model Order and Input Delay

Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate. While the investigation of stability of nontrivial solutions in 1 has received little attention from analytical view point, the influence of high-frequency excitation on nontrivial steady state has not been tackled. The stability occurs when two dominant roots of 3 are placed on the imaginary axis at the desired resonant frequency, while other roots remain in the stable left half of the complex plane.

Nontrivial Solutions Following [8], 1 can be viewed as the one mode model of a hinged-clamped beam. A first-order uniform expansion of the solution to 7 is sought in the form 2 1. The modulation equations of amplitude R and phase 9 of the periodic solutions are given at first-order approximation by the system dR 1 A.

Sound localization - Wikipedia

Solving for the fixed points ij 0. Substituting w by its value given by 6 , the condition 11 becomes 4n - 3 n - t -. The region II white zone corresponds to the existence domain of a stable limit cycle born by Hopf bifurcation when crossing from region I to region II. We have a dedicated site for Germany. Authors: Milton , John, Ohira , Toru. This introductory textbook is based on the premise that the foundation of good science is good data.

The educational challenge addressed by this introductory textbook is how to present a sampling of the wide range of mathematical tools available for laboratory research to well-motivated students with a mathematical background limited to an introductory course in calculus.

JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Mathematics Mathematical and Computational Biology. Free Preview. Uses real data Uses mathematical methods that are used in the laboratory Real laboratory exercises provided as supplementary material see more benefits.

Article information Source Electron. Citation Ruffino, Paulo R.

Export citation. Export Cancel. References [1] D. Cambridge University Press, Caraballo, P. Kloeden and J.

Mathematics as a Laboratory Tool

Real — Pulback and forward attractors for a damped wave equation with delays. Stochastic and Dynamics , vol. Catuogno, and P. Ruffino — Geometry of stochastic delay differential equations.