Abstract Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally，numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.
Received: 12 April 2007
Revised: 09 September 2007
Accepted manuscript online:
PACS:
05.40.-a
(Fluctuation phenomena, random processes, noise, and Brownian motion)
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10472091 and
10332030).
Cite this article:
Xu Wei(徐伟), Ma Shao-Juan(马少娟), and Xie Wen-Xian(谢文贤) Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter 2008 Chin. Phys. B 17 857
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