| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Research Abstract |
In this research, I developed the already proposed method to extract the influence of dynamical noise intrinsic to a system on chaos and proposed two methods, by which the extraction of the influence from the microscopic perspectives was expected to be possible.
A variety of points in a phase space structured by a scalar time series data obtained from Chua's electronic circuit model, were selected and devoted to the application to verify the fluctuation of singular values in the local space by using following two methods ;(1) a method to apply Singular Value Decomposition method to a local space(Local SVD), and(2) a method to use Support Vector Machine(SVM).
As a result, in the method(1), some important characteristics such as the difference of fluctuation among singular values that cannot be recognized in the macroscopic method are perceived. This means that the influence of dynamical noise in a local space is directly reflected in the results without averaging the influence in whole sp
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ace such as the macroscopic method and is useful to analyze the way of spreading of the influence of dynamical noise from a local space to a global one. In the method(2), the influence of dynamical noise can be extracted in the presence of measurement noise. Some parameters are used for this analysis. As a result, similar results are obtained in any parameters each other. The existence of optimal parameter values were indicated by recognizing the difference of fluctuation of singular values depending on such parameters.
Searching above-mentioned local space in the method(1) and treating high dimensional matrices in high dimensional space spends a longer time than expected before. Accordingly a program to solve the problem is being made. Here, for the sake of obtaining the high efficiency of numerical method, the improvement from the hardware side by parallelizing a computer system as a clustermachine and fromthe software side by introducing a parallel computing algorithm ; MPI(Message Passing Interface) and making and using a parallel program were executed.
While I made an electronic circuit to show chaotic behavior, applied the obtained data from this circuit to the macroscopic and microscopic methods, and compared those methods. As a result, it can be obtained that those results have qualitatively similar ones to each other. Although, in some cases, sufficient number of data cannot be acquired owing to the restriction to the experimental condition, unexpected external noise, and so on, the characteristic influence by dynamical noise can be obtained for even a small number of data. Especially, in the method(1), the characteristic influence to a local space can be more clearly extracted. Therefore, it can be said that the applicability of the proposed microscopic methods to realistic data was indicated. Less
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