scholarly journals Bifurcation analysis of vortex-induced vibration of low-dimensional models of marine risers

2021 ◽  
Vol 106 (1) ◽  
pp. 147-167
Author(s):  
Dan Wang ◽  
Zhifeng Hao ◽  
Ekaterina Pavlovskaia ◽  
Marian Wiercigroch
Keyword(s):  
Bifurcation Analysis ◽  
Vortex Induced Vibration ◽  
Marine Risers ◽  
Dimensional Models ◽  
Low Dimensional

scholarly journals Low-dimensional models of subcritical transition to turbulence

1997 ◽  
Vol 9 (4) ◽  
pp. 1043-1053 ◽  
Author(s):  
Jeffrey S. Baggett ◽  
Lloyd N. Trefethen
Keyword(s):  
Transition To Turbulence ◽  
Dimensional Models ◽  
Low Dimensional

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

Accurate low dimensional models for deterministic fluid systems driven by uncertain forcing

2011 ◽  
Vol 23 (9) ◽  
pp. 094101 ◽  
Author(s):  
G. Dergham ◽  
D. Sipp ◽  
J.-C. Robinet
Keyword(s):  
Fluid Systems ◽  
Dimensional Models ◽  
Low Dimensional

Low Dimensional Models, Wavelet Transforms and Control

1996 ◽  
pp. 271-331 ◽  
Author(s):  
N. Aubry ◽  
G. Berkooz ◽  
B. Coller ◽  
J. Elezgaray ◽  
P. Holmes ◽  
...  
Keyword(s):  
Wavelet Transforms ◽  
Dimensional Models ◽  
Low Dimensional ◽  
And Control
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