New scenario of the transition to chaos in degenerated systems

退化系统向混沌过渡的新场景

• 批准号: 11837006
• 负责人: MIKHAEL Tribelsky
• 金额: $ 1.92万
• 依托单位: University of Fukui
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11837006/
• 关键词: pattern formation; symmetry; degeneracy; Goldstone modes; dynamical chaos; International Exchange of Information; Germany, Kazakhstan, Russia, Spain, USA; pattern formation; Goldstone modes; symmetry breaking bifurcation; chaos; turbulence; no

During the term of the present grant a systematic study of the soft-mode turbulence (SMT) and related topics has been carried out. The following results have been obtained. In case of electroconvection in homeotropically aligned nematic layer SMT is caused by slow random long-wavelength modulations of a roll pattern. The temporal autocorrelation function for components of the order parameter is calculated and expressed in terms of probability density for random drift velocity of the pattern. It is shown that despite the problem has at least two different characteristic times associated with the slow pattern dynamics, only one of them enters into the autocorrelation function.The simplest nonlinear equation exhibiting SMT is the so-called Nikolaevskii equation. We employ numerical integration of this model to obtain detailed quantitative description of SMT. It is shown that SMT is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. T … More he Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter ε. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency. It is shown that if such a system undergoes instability against spatially periodic perturbations with a finite wavenumber, interplay of short-wavelength modes associated with the instability and long-wavelengths modes generated by the symmetry transformation affects the dynamics of the system dramatically. In particular, it may result in direct transition from a spatially uniform state to SMT, analogous to second order phase transition in equilibrium systems. Deep connection between SMT and the structure of the the dispersion equation for the relevant stability problem is revealed. A general phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed. The theory is based upon the fact that for most media these regions in the p-V plane are anomalously small. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rare faction is obtained and discussed.The dynamics of actual market prices is a very specific example of dynamical chaos. We apply our knowledge in the theory of dynamical chaos to quantitative analysis of this type of chaos. A number of particular examples (exchange rates USD vs. JPY, XAU vs. USD, oil, etc.) is considered in detail. It allows predicting the price dynamics in future with high accuracy. The main advantage of the approach is that the prediction error does not increase in the course of time. Less

在本项目期间，对软模湍流及其相关问题进行了系统的研究。取得了以下结果。在垂直排列的多层SMT中的电对流的情况下，由辊图案的缓慢随机长波长调制引起。计算序参数分量的时间自相关函数，并以图案随机漂移速度的概率密度表示。结果表明，尽管该问题至少有两个不同的慢斑图动力学特征时间，但只有一个特征时间进入自相关函数，表现慢斑图动力学的最简单的非线性方程是Nikolaevskii方程。我们采用这个模型的数值积分，以获得详细的定量描述SMT。结果表明，SMT的特点是不同的空间尺度的平滑的相互作用，与缺陷产生是不重要的。不 ...更多信息 对于控制参数ε的固定值，计算了几种系统尺寸的李雅普诺夫指数。的李雅普诺夫维数和Kolmogorov-Sinai熵的计算和都表现出广泛和microextensive缩放。分布函数满足高斯统计在小波数和小频率。结果表明，如果这样的系统经历对空间周期性扰动与有限波数的不稳定性，与不稳定性和长波长的对称变换产生的模式的相互作用的短波长模式显着影响系统的动态。特别是，它可以导致从空间均匀状态到SMT的直接转变，类似于平衡系统中的二级相变。SMT和结构的色散方程的相关的稳定性问题之间的深层连接被揭示。本文发展了等熵线光滑凸性损失区域中流体动力波的一般唯象理论。该理论基于这样的事实，即对于大多数介质，p-V平面中的这些区域非常小。推导并分析了相应的广义Burgers方程。得到了稀有类定常冲击波方程的精确解，并讨论了该方程的精确解，实际市场价格的动态是动态混沌的一个非常具体的例子。我们运用我们的知识，在动力学混沌理论定量分析这种类型的混沌。一些具体的例子（汇率美元兑日元，XAU兑美元，石油等）被详细考虑。它允许以高精度预测未来的价格动态。该方法的主要优点是预测误差不会随着时间的推移而增加。少

项目成果

M.I.Tribelsky: "Predictability of market prices"Empirical Science of Financial Fluctuations. The Advent of Econophysics, edited by H. Takayasu (Springer, Tokyo, Berlin, etc.). 241-249 (2001)

M.I.Tribelsky：“市场价格的可预测性”金融波动的实证科学。

M.I.Tribelsky: "Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes : General Phenomenological Theory"Physical Review Letters. 86. 4037-4040 (2001)

M.I.Tribelsky：“等熵凸性平滑损失区域中的流体动力波：一般现象学理论”物理评论快报。

M. Tribelsky, Y. Harada, N. Makarenko, and Y. Kuandykov: "Predictability of market prices"Empirical Science of Financial Fluctuations. The Advent of Econoohysics, edited by H. Takayasu (Springer, Tokyo, Berlin, etc.). 241-249 (2001)

M. Tribelsky、Y. Harada、N. Makarenko 和 Y. Kuandykov：“市场价格的可预测性”金融波动的实证科学。

H.Xi: "Extensive Chaos in the Nikolaevskii Model"Phys.Rev.E.(Rapid Comm.). 62. 17-20 (2000)

H.Xi：“尼古拉耶夫斯基模型中的广泛混沌”Phys.Rev.E.(Rapid Comm.)。

M.I.Tribelsky: "Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes : General Phenomenological Theory"Phys. Rev. Lett.. 86. 4037-4040 (2001)

M.I.Tribelsky：“等熵凸性平滑损失区域中的流体动力波：一般唯象理论”Phys。