Dynamical system visualization and analysis via performance maps

Abstract

Visualization techniques are common in the study of chaotic motion. These techniques range from simple time graphs and phase portraits to robust Julia sets, which are familiar to many as 'fractal images.' The utility of the Julia sets rests not in their considerable visual impact, but rather, in the color-coded information that they display about the dynamics of an iterated function. In this paper, a paradigm termed the performance map is presented, which is derived from the familiar Julia set. Performance maps are generated automatically for control or other dynamical system models over ranges of system parameters. The resulting visualizations require a minimum of a priori knowledge of the system under evaluation. By the use of color-coding, these images convey a wealth of information to the informed user about dynamic behaviors of a system that may be hidden from all but the expert analyst.