Computing of 3D Bifurcation Diagrams With Nvidia CUDA Technology

Abstract

This paper presents three-dimensional bifurcation diagrams in the form of a point cloud. The diagrams were created by means of parallel calculations using the electric arc model. A simple dynamic DC electric model that can show complex bifurcations with periodic and chaotic responses is presented. The Nvidia CUDA massively parallel architecture was used to perform the calculations. The paper shows cross-sections of the bifurcation cloud obtained as a result of calculations. It also presents an interactive tool specially developed to visualize the cloud. The reader can access the tool by using the Web address provided in this paper. This tool enables to freely specify the plane and axis of the cut in order to obtain the desired cross-section of the cloud — it is possible to obtain exactly such diagrams as those presented in the paper, as well as many others.

Keywords

• Electric arc
• 3D bifurcation diagrams
• cloud of points
• Nvidia CUDA
• ODE
• parallel computing