Subharmonic and homoclinic bifurcations in a parametrically forced pendulum

1985 ◽  
Vol 16 (1) ◽  
pp. 1-13 ◽  
Author(s):  
B.P. Koch ◽  
R.W. Leven
Keyword(s):  
Homoclinic Bifurcations ◽  
Forced Pendulum

Truncated-fractal basin boundaries in forced pendulum systems

1988 ◽  
Vol 60 (8) ◽  
pp. 665-668 ◽  
Author(s):  
Matthew Varghese ◽  
James S. Thorp
Keyword(s):  
Fractal Basin Boundaries ◽  
Forced Pendulum ◽  
Basin Boundaries

scholarly journals An asymptotic symmetry of the rapidly forced pendulum

1991 ◽  
Vol 51 (1-3) ◽  
pp. 109-118 ◽  
Author(s):  
Yi-Hua Chang ◽  
Harvey Segur
Keyword(s):  
Asymptotic Symmetry ◽  
Forced Pendulum

scholarly journals Minimal Universal Model for Chaos in Laser with Feedback

2021 ◽  
Vol 31 (04) ◽  
pp. 2130013
Author(s):  
Riccardo Meucci ◽  
Stefano Euzzor ◽  
F. Tito Arecchi ◽  
Jean-Marc Ginoux
Keyword(s):  
Laser Physics ◽  
Nonlinear Oscillator ◽  
Three Dimensional ◽  
Universal Model ◽  
Type Formula ◽  
The Third ◽  
Proposed Model ◽  
Homoclinic Bifurcations ◽  
Electronic Implementation ◽  
Different Time Scales

We revisit the model of the laser with feedback and the minimal nonlinearity leading to chaos. Although the model has its origin in laser physics, with peculiarities related to the [Formula: see text] laser, it belongs to the class of the three-dimensional paradigmatic nonlinear oscillator models giving chaos. The proposed model contains three key nonlinearities, two of which are of the type [Formula: see text], where [Formula: see text] and [Formula: see text] are the fast and slow variables. The third one is of the type [Formula: see text], where [Formula: see text] is an intermediate feedback variable. We analytically demonstrate that it is essential for producing chaos via local or global homoclinic bifurcations. Its electronic implementation in the range of kilo Hertz region confirms its potential in describing phenomena evolving on different time scales.

THE OSCILLATION–ROTATION ATTRACTORS IN THE FORCED PENDULUM AND THEIR PECULIAR PROPERTIES

2002 ◽  
Vol 12 (01) ◽  
pp. 159-168 ◽  
Author(s):  
WANDA SZEMPLIŃSKA-STUPNICKA ◽  
ELŻBIETA TYRKIEL
Keyword(s):  
Control Parameter ◽  
Fractal Structure ◽  
Basins Of Attraction ◽  
Parameter Plane ◽  
System Control ◽  
Periodic Force ◽  
Forced Pendulum ◽  
Insight Into

The paper is aimed at exploration of the properties of the oscillation–rotation attractors in the dissipative pendulum driven by external periodic force. The study of regions of existence of the orbits in the system control parameter plane, coexistence with other attractors, fractal structure of their basins of attraction, and the role they play in the onset of the tumbling chaos, give an insight into some peculiar features of the oscillation–rotation attractors and their bifurcational structures.

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