Codimension Two Bifurcation in an Approximate Model for Delayed Robot Control

1991 ◽  
pp. 155-159
Author(s):  
G. Haller ◽  
G. Stépán
Keyword(s):  
Robot Control ◽  
Approximate Model ◽  
Codimension Two ◽  
Codimension Two Bifurcation

NEW PHENOMENA IN THE NEIGHBORHOOD OF THE CODIMENSION-TWO BIFURCATION IN THE TWIN-WELL DUFFING OSCILLATOR

2000 ◽  
Vol 10 (06) ◽  
pp. 1367-1381 ◽  
Author(s):  
W. SZEMPLIŃSKA-STUPNICKA ◽  
A. ZUBRZYCKI ◽  
E. TYRKIEL
Keyword(s):  
Bifurcation Point ◽  
Chaotic Attractor ◽  
Duffing Oscillator ◽  
Codimension Two ◽  
Periodic Attractors ◽  
The Cross ◽  
Complex Phenomena ◽  
New Phenomena ◽  
Secondary Bifurcations ◽  
Codimension Two Bifurcation

In this paper, we study effects of the secondary bifurcations in the neighborhood of the primary codimension-two bifurcation point. The twin-well potential Duffing oscillator is considered and the investigations are focused on the new scenario of destruction of the cross-well chaotic attractor. The phenomenon belongs to the category of the subduction scenario and relies on the replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. The exploration of a sequence of accompanying bifurcations throws more light on the complex phenomena that may occur in the neighborhood of the primary codimension-two bifurcation point. It shows that in the close vicinity of the point there appears a transition zone in the system parameter plane, the zone which separates the two so-far investigated scenarios of annihilation of the cross-well chaotic attractor.

The Double Seesaw Oscillator in a Windfield: Theory and Experiments

1997 ◽  
Author(s):  
A. H. P. van der Burgh ◽  
T. I. Haaker ◽  
B. W. van Oudheusden
Keyword(s):  
Equilibrium State ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Typical Result ◽  
Resonant Case ◽  
Accurate Model ◽  
Codimension Two ◽  
Model Equations ◽  
Theory And Experiments ◽  
Codimension Two Bifurcation

Abstract In this paper the dynamics of an oscillator with two degrees-of-freedom of a double seesaw type in a windtunnel is studied. Model equations for this aeroelastic oscillator are derived and an analysis of these equations is given for the non-resonant case. A typical result is a (local codimension two) bifurcation which describes the transfer from the unstable equilibrium state to one of the two normal modes of the oscillator. Some experimental results are presented from which on may conclude that more accurate model equations should be developed.

The codimension-two bifurcation for the recent proposed SD oscillator

2009 ◽  
Vol 59 (1-2) ◽  
pp. 19-27 ◽  
Author(s):  
Ruilan Tian ◽  
Qingjie Cao ◽  
Shaopu Yang
Keyword(s):  
Codimension Two ◽  
Sd Oscillator ◽  
Codimension Two Bifurcation
Sign in / Sign up

Export Citation Format

Share Document