ISSN:
1573-269X
Keywords:
double pendulum system
;
double Hopf bifurcation
;
stability
;
chaos
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A double pendulum system is studied for analyzing the dynamic behaviour near a critical point characterized by nonsemisimple 1:1 resonance. Based on normal form theory, it is shown that two phase-locked periodic solutions may bifurcate from an initial equilibrium, one of them is unstable and the other may be stable for certain values of parameters. A secondary bifurcation from the stable periodic solution yields a family of quasi-periodic solutions lying on a two-dimensional torus. Further cascading bifurcations from the quasi-periodic motions lead to two chaoses via a period-doubling route. It is shown that all the solutions and chaotic motions are obtained under positive damping.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008347523779
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