Experimental Mathematics for Constitution and Computation in Complex Systems

复杂系统构成与计算实验数学

• 批准号: 07309017
• 负责人: TSUDA Ichiro
• 金额: $ 1.73万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07309017/
• 关键词: Concurrent process; Coupled map lattices; Chaotic Itinerancy; Langevin equations; Variational principle; Category theory; Logic-dynamics transformation; Internal observers; Chaotic dynamical systems; 論理; 結合写像格子; 確率過程; 幾何学; セル力学系

Experimental mathematics method for constitution and computation in complex systems were developed. Complex systems are defined as systems which cannot be analyzed by reductionist's method, that is, a method of "divide-and-concur" that ancient Roman emperors adopted, but rather be easily understood via constitution or its process of such systems.Many researchers from various kinds of research fields gathered together in Sapporo, and discussed intensively and extensively what a central method should be. Several methods were clarified.1. Coupled map lattices are useful for the purpose of seeking a universality at intermediate levles which is hidden at both microscopic and macroscopic levels.2. A new type of stochastic theory is necessary for analysing a high dimensional chaos.3. A geometric and variational method is useful for a mechanism of high-dimensional spatio-temporal patterns.4. Logics and category theory is a tool for concurrent process of network systems.5. A transformation between logics and dynamics is effective for a system where a different levels of dynamics interfere.6. An observer-oriented theory is essential for constructing an adequate language for complex systems.

提出了复杂系统构成与计算的实验数学方法。复杂系统被定义为不能用还原主义的方法，即古罗马皇帝采用的“分治法”来分析的系统，而是通过这种系统的构成或其过程来容易理解的系统。来自不同研究领域的许多研究者聚集在札幌，就中心方法应该是什么进行了深入而广泛的讨论。澄清了几种方法。耦合映射格对于寻求隐藏在微观和宏观水平上的中间水平的通用性是有用的。分析高维混沌需要一种新的随机理论。几何和变分方法对高维时空模式的机制是有用的。逻辑范畴论是研究网络系统并发过程的工具。逻辑与动力学之间的转换对于有不同层次的动力学干扰的系统是有效的。面向观察者的理论对于为复杂系统构建合适的语言是必不可少的。

项目成果

I.Tsuda: "The form of chaos in the noisy brain can manifest function" Behavioral and Brain Sciences. 19・2. 309-309 (1996)

I.Tsuda：“嘈杂的大脑中的混乱形式可以体现功能”《行为与脑科学》19・2（1996）。

Y. Okabe: "Application of the theory of KM_2O-Langevin equations to the nonlinear prediction problem for the one-dimensional strictly stationary time series" J. Math. Soc. Japan. 47・2. 349-367 (1995)

Y. Okabe：“KM_2O-Langevin 方程理论在一维严格平稳时间序列的非线性预测问题中的应用”J. Math. 47・2 (1995)。

金子邦彦: "複雑系のカオス的シナリオ" 朝倉書店, 297 (1996)

金子邦彦：“复杂系统的混沌场景”朝仓书店，297（1996）

M.Taniguchi: "Stability and characteristic wavelength of planar interfaces" Proc.of Royal Society of Edinburgh. 126A. 117-145 (1996)

M.Taniguchi：“平面界面的稳定性和特征波长”Proc.of Royal Society of Edinburgh。

Y. Okada: "Application of the theory of KM_2O - Langevin equations to the nonlinear prediction problem for the one-dimensional strictly stationary time series" J. Math. Soc, Japan. 47・2. 349-367 (1995)

Y. Okada：“KM_2O - Langevin 方程理论在一维严格平稳时间序列的非线性预测问题中的应用”J. Math，日本 47・2。