Visualization of stability of dynamical systems by 3D graphics supported by cluster computing

Takashi Funasaka, Masami Iwase, Katsuki Fujisawa, Shoshiro Hatakeyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 n+1 = z 2 n + C can be stabilized, that is Mandelbrot and Julia sets, respectively.

Original languageEnglish
Title of host publicationProceedings of the Third Workshop - 2005 IEEE Intelligent Data Acquisition and Advanced Computing Systems
Subtitle of host publicationTechnology and Applications, IDAACS 2005
Pages588-592
Number of pages5
DOIs
Publication statusPublished - Dec 1 2007
Externally publishedYes
Event3rd IEEE Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005 - Sofia, Bulgaria
Duration: Sep 5 2005Sep 7 2005

Other

Other3rd IEEE Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005
CountryBulgaria
CitySofia
Period9/5/059/7/05

Fingerprint

Cluster computing
3D Graphics
Cluster Computing
Field programmable gate arrays (FPGA)
Drawing (graphics)
Dynamical systems
Visualization
Dynamical system
Field Programmable Gate Array
Nonlinear systems
Stabilization
High Performance
Mandelbrot set
Calculator
Julia set
One Dimension
High-dimensional
Nonlinear Systems
Projection
Real-time

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Vision and Pattern Recognition
  • Theoretical Computer Science

Cite this

Funasaka, T., Iwase, M., Fujisawa, K., & Hatakeyama, S. (2007). Visualization of stability of dynamical systems by 3D graphics supported by cluster computing. In Proceedings of the Third Workshop - 2005 IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005 (pp. 588-592). [4062203] https://doi.org/10.1109/IDAACS.2005.283052

Visualization of stability of dynamical systems by 3D graphics supported by cluster computing. / Funasaka, Takashi; Iwase, Masami; Fujisawa, Katsuki; Hatakeyama, Shoshiro.

Proceedings of the Third Workshop - 2005 IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005. 2007. p. 588-592 4062203.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Funasaka, T, Iwase, M, Fujisawa, K & Hatakeyama, S 2007, Visualization of stability of dynamical systems by 3D graphics supported by cluster computing. in Proceedings of the Third Workshop - 2005 IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005., 4062203, pp. 588-592, 3rd IEEE Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005, Sofia, Bulgaria, 9/5/05. https://doi.org/10.1109/IDAACS.2005.283052
Funasaka T, Iwase M, Fujisawa K, Hatakeyama S. Visualization of stability of dynamical systems by 3D graphics supported by cluster computing. In Proceedings of the Third Workshop - 2005 IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005. 2007. p. 588-592. 4062203 https://doi.org/10.1109/IDAACS.2005.283052
Funasaka, Takashi ; Iwase, Masami ; Fujisawa, Katsuki ; Hatakeyama, Shoshiro. / Visualization of stability of dynamical systems by 3D graphics supported by cluster computing. Proceedings of the Third Workshop - 2005 IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2005. 2007. pp. 588-592
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