Double Hopf Bifurcations and Chaos of a Nonlinear Vibration System |
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Authors: | Bi Qinsheng Yu Pei |
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Institution: | (1) Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada, R6A 5B7 |
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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. |
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Keywords: | double pendulum system double Hopf bifurcation stability chaos |
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