Quantization of chaotic phenomena by the chaos degree

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400216
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo University of Science, Yamaguchi
• Principal Investigator: Inoue Kei 山口東京理科大学, 工学部, 教授 (70307700)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: カオスの定量化 / カオス尺度 / リアプノフ指数 / 情報理論

Outline of Final Research Achievements

Lyapunov exponent is well used as a criterion to measure the degree of chaos of dynamical systems.There exists such a certain chaotic dynamical system that it is often difficult to compute its Leapunov exponent. In such situations we tried to introduce such an information quantity that we can measure chaos of dynamical systems. From the information theoretical point of view, the chaos can be considered as an information generative process. Following that idea, an information quantity, which is called entropic chaos degree, was introduced.
In this study, the following topics were mainly studied: (1) basic properties of the chaos degree in classical discrete systems was shown, (2) how to treat quasi-periodic orbits was established by using the entropic chaos degree, and (3) evaluations of generalized multibaker maps with boundary conditions were considered by the chaos degree. Now an analysis of chaos for a time series obtained from some experiments is tried by the chaos degree.

Free Research Field

カオス、フラクタル、情報数理