Density-Colored Bifurcation Diagrams — A Complementary Tool for Chaotic Map Analysis

Abstract

This work presents a numerical method to color the bifurcation diagram of any discrete map, based on the distribution of the map’s values in its domain. This density-colored diagram reveals information on the uniformity of the map’s value distribution across its domain set, as a bifurcation parameter is increased. This diagram can serve as a complementary visual tool for the analysis of chaotic maps, and can be vital for the application of chaotic dynamics.