High-codimensional static bifurcations of strongly nonlinear oscillator
Zhang Qi-Chang (张琪昌), Wang Wei (王 炜), Liu Fu-Hao (刘富豪)
Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China; State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China
Abstract The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing--van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with $Z_{2}$ symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
Received: 16 May 2008
Revised: 03 June 2008
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10872141) and the
Specialized Research Fund for the Doctoral Program of Higher
Education of China (Grant No 20060056005).
Cite this article:
Zhang Qi-Chang (张琪昌), Wang Wei (王 炜), Liu Fu-Hao (刘富豪) High-codimensional static bifurcations of strongly nonlinear oscillator 2008 Chin. Phys. B 17 4123
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