Continuous-Time Density-Colored Bifurcation Diagrams

This work extends the construction of the density-colored bifurcation diagrams proposed by [Moysis et al., 2023] to continuous-time systems, and discusses several variations of them. These diagrams depict the histogram density of the local maxima in the underlying time series solution, using color grading. It thus complements the standard bifurcation diagram, by depicting information about the statistical distribution of the solution across the mapping domain. Several variations of these diagrams can be generated, by changing the colormap scaling, or by computing the statistical distribution of the time series locally or globally. These variations are also discussed. Numerical examples are provided for three chaotic systems. Moreover, MATLAB and Python codes are provided for generating the diagrams.