NDLI: Visualization of Stability of Dynamical Systems by 3D Graphics Supported by Cluster Computing

Content Provider	IEEE Xplore Digital Library
Author	Funasaka, T. Iwase, M. Fujisawa, K. Hatakeyama, S.
Copyright Year	2005
Description	Author affiliation: Dept. of Comput. & Syst. Eng., Tokyo Denki Univ., Tokyo (Funasaka, T.; Iwase, M.)
Abstract	The stabilization of nonlinear systems depend strongly on the initial state and the parameters of the systems. The initial state and the parameters with which the system is stabilized can be distinguished by the geometrical structure. It is, however, difficult and sometimes impossible to analyze the structure analytically. Therefore it comes important to show and analyze the structure of the parameters and initial states numerically and visually. In this paper, we present a method to draw and visualize such region and structure in the three dimensional space. In general, the projection of the original high-dimensional space to the lower dimension one is required for using visual analysis. Thus, it is convenient that the viewpoint can be moved, without time loss, in the direction where analyst would like to see. As often as the viewpoint moves, the recomputation as quick as possible is required to realize the quick motion of viewpoint. It is, however, obvious that lots of computation and time are taken to draw the region. Therefore, high performance calculators are needed to realize the real-time drawing. In order to overcome this problem, FPGA and cluster-computing is used in this paper. Then it is demonstrated by illustrative examples that FPGA and cluster-computing shows high performance to draw the region of the parameters and initial state in 3D with which z : + c can be stabilized, that is Mandelbrot and Julia sets, respectively.
Starting Page	588
Ending Page	592
File Size	5011855
Page Count	5
File Format	PDF
ISBN	0780394453
DOI	10.1109/IDAACS.2005.283052
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-09-05
Publisher Place	Bulgaria
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Visualization Graphics Field programmable gate arrays Nonlinear systems Stability analysis Computer networks Concurrent computing Calculators Nonlinear control systems Control systems 3D graphics Fracta Cluster-computing FPGA Homogenous transformation
Content Type	Text
Resource Type	Article

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