权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Analysis of Chaos and Fractals via Photonic Computing and Approaches of Fuzzy Mathematical Method

通过光子计算和模糊数学方法分析混沌和分形

基本信息

批准号：
16500128
负责人：
SAITO Seiji
金额：
$ 2.24万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

项目摘要

Henon mentions that there exists the structure of a Cantor set in "A Two-dimensional Mapping with a Strange Attractor," Commun. Math. Phys., 30, pp69-77, 1976 as follows : Figure 4 to 6 strongly suggest that the process of multiplication of "curves" will continue indefinitely, and that each apparent" curve" is in fact made of an infinitely of quasi-parallel curves. Moreover these figures indicate the existence of a hierarchical sequence of "levels," the structure being practically identical at each level save for a scale factor. Our goal of this research is to show the relationship between chaos and fractals and to establish a criterion for the existence of chaos arising from well-known mappings in higher order dynamical systems.Marotto gave a criterion for the existence of chaos in finite dimensional dynamical systems where the absolute values of eigenvalues to the Jacobi matrix at its fixed point are larger than 1 in J. Math. Anal. Appl. 63, pp199-223, 1978. It is impossible to apply … More the criterion to the Gumowski-Mira's mapping with parameters a=0.008, b=0.05 and μ being through -0.89 to -0.995, in detail see S, Saito and H.Ishii : "On Chaos of the Warlas' Adjustment Difference Equation", Economic papers of Kobegakuin (to appear). Because in some case of parameters the absolute values of the eigenvalues are smaller than 1.In this research we considered the Gumowski-Mira's mapping with absolute values of eigenvalues being smaller than 1 and also had a lot of simulation data of the mapping. In our approaches we study the structure of Cantor sets and we are establishing the existence criterion of Li-Yorke chaos of the mapping via two methods : fuzzy analysis and photonic method.In fuzzy approach we had several results on qualitative criteria for the existence and uniqueness of solutions to boundary fuzzy differential equations. We got practical criteria for fuzzy facility location problems with preference of candidate sites. Moreover we gave results on "Photonic DNA computing : concept and implementation" in the viewpoint of photonic array computing.Our aims of this research are to get criteria for the existence of chaos of the Gumowski-Mira's mapping and to propose a generator of pseudo-random number for encryption by applying the results on analyzing chaos properties, specifically the sensitive dependence of initial data. We had some suitable and applicable results for this research in our papers of the references of this abstract. Less

Henon提到，在“一个二维映射与一个奇怪的吸引子，”Commun。数学物理，30，pp 69 -77，1976如下：图4至6强烈表明，“曲线”的倍增过程将无限地继续下去，并且每个明显的“曲线”实际上是由无限的准平行曲线组成的。此外，这些数字表明存在一个“层次”的层次序列，除了比例因子之外，每个层次的结构实际上是相同的。Marotto在J. Math. Anal.中给出了Jacobi矩阵在不动点的特征值绝对值大于1的有限维动力系统存在混沌的一个判别准则。Appl. 63，pp199-223，1978。不可能申请 ...更多信息参数a=0.008，B=0.05，μ从-0.89到-0.995的Gumowski-Mira映射的判别准则，详见S，Saito和H.石井：“On Chaos of the Warlas' Adjustment Difference Equation”，Economic papers of Kobegakuin（待发表）。因为在某些参数情况下，特征值的绝对值小于1。本研究考虑了特征值的绝对值小于1的Gumowski-Mira映射，并对该映射进行了大量的模拟。在我们的方法中，我们研究了Cantor集的结构，用模糊分析和光子学方法建立了该映射的Li-Yorke混沌的存在性判据，在模糊方法中，我们得到了边界模糊微分方程解的存在性和唯一性的定性判据。得到了具有候选选址偏好的模糊设施选址问题的实用准则。我们的研究目的是通过对Gumowski-Mira映射的混沌特性的分析，特别是对初始数据的敏感依赖性的分析，得到Gumowski-Mira映射混沌存在的判据，并提出一种用于加密的伪随机数生成器。在我们的论文中，我们得到了一些适合本研究的结果。少

项目成果

期刊论文数量（50）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Fuzzy Facility Location Problem with Preference of Candidate Site and A-Distance

具有候选地点偏好和A距离的模糊设施选址问题

DOI：
发表时间：
2005
期刊：
Proceedings of 11^<th> Asia Pacific Management Conference
影响因子：
0
作者：
H.Ishli;Yung Lung Lee;Kuang Yih Yeh
通讯作者：
Kuang Yih Yeh

On Schauder's Fixed Point Theorem in Sets of Fuzzy Numbers and Its Extension

模糊数集中Schauder不动点定理及其推广

DOI：
发表时间：
2004
期刊：
Proceeding of the 7^<th> Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty
影响因子：
0
作者：
Draguna;M.R.;Nakamura;T;Shibasaki;A.et al.;S.Saito
通讯作者：
S.Saito

On Schauder's Fixed Point Theorem in Complete Metric Spaces of Fuzzy Numbers and Applications to Fuzzy Boundary Value Problems

模糊数完备度量空间中Schauder不动点定理及其在模糊边值问题中的应用

DOI：
发表时间：
2004
期刊：
International Conference on Fuzzy Systems, AFSS'2004(Asian Fuzzy Systems Society)
影响因子：
0
作者：
Zhaoshui He;Shengli Xie;Shuxue Ding(丁数学);Andrzej Cichocki;S.Saito
通讯作者：
S.Saito

Visual Approaches for Numerical Analysis Concerning Fuzzy Differential Equations

模糊微分方程数值分析的可视化方法