DocumentCode :
3238849
Title :
Visualization of Stability of Dynamical Systems by 3D Graphics Supported by Cluster Computing
Author :
Funasaka, Takashi ; Iwase, Masami ; Fujisawa, Katsuki ; Hatakeyama, Shoshiro
Author_Institution :
Dept. of Comput. & Syst. Eng., Tokyo Denki Univ., Tokyo
fYear :
2005
fDate :
5-7 Sept. 2005
Firstpage :
588
Lastpage :
592
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.
Keywords :
computer graphics; control engineering computing; data visualisation; field programmable gate arrays; nonlinear dynamical systems; stability; workstation clusters; 3D graphics; FPGA; cluster computing; dynamical system stability; geometrical structure; nonlinear system stabilization; visual analysis; Calculators; Computer networks; Concurrent computing; Control systems; Field programmable gate arrays; Graphics; Nonlinear control systems; Nonlinear systems; Stability analysis; Visualization; 3D graphics; Cluster-computing; FPGA; Fracta; Homogenous transformation;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, 2005. IDAACS 2005. IEEE
Conference_Location :
Sofia
Print_ISBN :
0-7803-9445-3
Electronic_ISBN :
0-7803-9446-1
Type :
conf
DOI :
10.1109/IDAACS.2005.283052
Filename :
4062203
Link To Document :
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