Applications of Chaos and bifurcations in delayd differential equations

混沌和分岔在时滞微分方程中的应用

基本信息

批准号：
05836004
负责人：
TOKUNAGA Ryuji
金额：
$ 1.47万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05836004/
关键词：
chaos bifurcations learning prediction non lnear neural networks bifurcation diagram parameterized family

项目摘要

The objective of this research is to study and develop applications of chaos and bifurcations of delayd differential equations.In the first stage, a delayd differential system with back propagation learning algorithm is applied to deterministic nonlinear prediction. Since its degree of freedom is infinite, very complicated patterns can be learned and generated by the delayd differential systems. The prediction system is tested against several chaotic dynamical systems in order to show its prediction capabilities. [1]In the second stage, using the proposed system, irregular vibrations in the Japanese vowel sounds are investigated in the light of fractal dimension, Lyapnov exponents, and KS-entropy. Consequently, numerical evidence which suggests their relationship with deterministic chaos are obtained. [2]In the third srage, a novel inverse problem for chaotic dynamics is formulated and studied. And propose an algorithm to reconstruct qualitatively similar parametrized family of dynamical systems only from several time-waveforms measured from unknown parametrized family of dynamical systems. This algorithm is essentially based on nonlinear prediction technique and principal component analysis. In order to show its capability, it is tested against several parametrized family of discrete dynamical systems. [3][4][5]In the fourth stage, proposed algorithm is extended, and applied to a time-continuous system. Here, effect of observational noise is also investigated, and its robustness is numerically confirmed. Since this improved algorithm is extremely simple, it is possible to apply this technique to system indentification and time-waveform recognition of unknown chaotic dynamics.

这项研究的目的是研究和开发混乱和延迟微分方程的分叉的应用。在第一阶段，将带有背部传播学习算法的延迟差分系统应用于确定性的非线性预测。由于其自由度是无限的，因此可以通过延迟差异系统来学习和生成非常复杂的模式。为了显示其预测能力，对几个混沌动力学系统进行了预测系统。 [1]在第二阶段，使用所提出的系统，根据分形维度，Lyapnov指数和KS-肠道，研究日本元音声音中的不规则振动。因此，获得了表明它们与确定性混乱关系的数值证据。 [2]在第三次Srage中，对混乱动力学的新型逆问题进行了制定和研究。并提出了一种算法，以从定性上相似的动态系统的参数化家族重建，仅从来自未知参数化的动态系统的参数化家族测得的几个时间波。该算法基本上基于非线性预测技术和主成分分析。为了显示其能力，它将针对几个离散动力学系统的几个参数化家族进行测试。 [3] [4] [5]在第四阶段，提出的算法被扩展并应用于及时的系统。在这里，还研究了观察噪声的效果，并在数值上确认其鲁棒性。由于这种改进的算法非常简单，因此可以将此技术应用于系统凹痕和对未知混沌动力学的时间波动识别。