Proceeding of International Conference
Quentin Brandon, Toshiyuki Kumano, Tetsushi Ueta, Method of repellers detection by applied computation over basin of attraction, Proc. NDES2007, 241-244, Tokushima, July 2007.
Abstract: This paper proposes a new visualization method for chaotic attractors and detection of repellers in the basin of attraction of discrete nonlinear dynamical systems. Conventionally it is expressed by plotting the solution orbit into a plane as a set of dots. In the case of color figures, a pixel is usually colored based on the location of the orbit, hitting statistics, and so on. In some other approaches, a pixel is colored by n-time map direction. This method is called directional coloring. However, it requires much time to calculate both the solution and the n-time map direction. We use an argument defined by a current orbit and an n-time mapped point is used for coloring in initial plane. This method can decrease the computation time, and can render a direction map where all solutions within the range arbitrarily specified. This method can visualize repeller as well as directional coloring. The position of repellers can be detected by automatically setting up the candidate point based on visualized repellers.