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强迫布鲁塞尔振子中的阵发混沌

王光瑞 陈式刚 郝柏林

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强迫布鲁塞尔振子中的阵发混沌

王光瑞, 陈式刚, 郝柏林

INTERMITTENT CHAOS IN THE FORCED BRUSSELATOR

WANG GUANG-RUI, CHEN SHI-GANG, HAO BAI-LIN
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  • 用数值计算证实了在周期外力作用下的三分子反应模型(布鲁塞尔振子)中存在着走向混沌状态的阵发道路。研究了阵发混沌的发展过程。讨论了数值研究中区分阵发混沌和暂态过程的方法。我们的工作进一步说明,原来在参数空间中发现的嵌在混乱带中的大片周期为3的区域(以及周期为4,5,6,7等的较小区域),对应于一维非线性映象相像的切分岔)每个切分岔开始前均可看到阵发混沌。因此,走向混沌的倍周期分岔道路和阵发道路乃是孪生现象,应在更多的由非线性微分方程描述的系统中观察到。
    We show numerically that in the model of trimolecular reaction under external periodic force (the forced Brusselator) there exists the intermittent route to chaos. The time development of intermittent chaos and the method to distinquish intermittency from transients are studied. The large region of period 3 in the parameter space, discovered previously in the forced Brusselator, as well as smaller regions of periods 4, 5, 6 … etc., correspond to tangent bifurcations in one-dimensional mappings. Intermittency appears just before the start of every tangent bifurcation. Therefore, the period-doubling and the intermittent routes to chase are "twin" phenomena and they should be observable in many other systems described by nonlinear differential equations.
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出版历程
  • 收稿日期:  1982-08-20
  • 刊出日期:  2005-07-21

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