Can We Obtain a Fractional Lorenz System from a Physical Problem? |
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引用本文: | 杨帆,朱克勤.Can We Obtain a Fractional Lorenz System from a Physical Problem?[J].中国物理快报,2010,27(12):124-127. |
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作者姓名: | 杨帆 朱克勤 |
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基金项目: | Supported by the National Natural Science Foundation of China under Grant No 10972117. |
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摘 要: | A new fractional-order Lorenz system is obtained from the convection of fractional Maxwell fluids in a circular loop. This is the first fractional-order dynamical system derived from an actual physical problem, and rich dynamical properties are observed. In the case of short fluid relaxation time, with the decreasing effective dimension ∑, we find a critical value of the effective dimension ∑cr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value ∑cr2(∑cr2 〈∑cr1) at which the regular dynamics of the system returns to the chaotic one. In the case of long relaxation time, the phenomenon of overstability is observed and the decrease of ∑ is found to delay the onset of it.
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关 键 词: | Lorenz系统 物理问题 Maxwell流体 分式 弛豫时间 混沌动力学 分数阶 动力系统 |
收稿时间: | 2010-7-14 |
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