中国物理B ›› 2008, Vol. 17 ›› Issue (3): 857-864.doi: 10.1088/1674-1056/17/3/022

• GENERAL • 上一篇    下一篇

Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter

徐伟, 马少娟, 谢文贤   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
  • 收稿日期:2007-04-12 修回日期:2007-09-09 出版日期:2008-03-04 发布日期:2008-03-04
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10472091 and 10332030).

Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter

Xu Wei(徐伟), Ma Shao-Juan(马少娟)†, and Xie Wen-Xian(谢文贤)   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
  • Received:2007-04-12 Revised:2007-09-09 Online:2008-03-04 Published:2008-03-04
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10472091 and 10332030).

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摘要： 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.

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.

Key words: random parameter, stochastic Duffing system, stochastic period-doubling bifurcation, orthogonal polynomial approximation

中图分类号:  (Fluctuation phenomena, random processes, noise, and Brownian motion)

  • 05.40.-a
02.30.Oz (Bifurcation theory) 02.50.Ey (Stochastic processes) 05.45.Gg (Control of chaos, applications of chaos)