Convex Hull as a method for Characterizing Chaotic Systems
DOI:
https://doi.org/10.66131/JDSC1320261-10Keywords:
Chaotic systems, Dynamical Systems, convex hull, fractal dimension, Chua attractorAbstract
This work uses convex hulls to characterize geometric variations in chaotic systems. Calculating the area or volume of the convex hull provides a global quantitative descriptor for the spatial extent of the attractor. This provides a metric that complements conventional measurements and forms the basis for quantitative behavioral comparisons. The results presented are based on comparing the behavior of different versions of Chua systems that have similar attractor shapes and very similar values in the Kaplan-Yorke and fractal dimensions, but whose behavior differs greatly when the spatial component is analyzed. This work emphasizes the consideration of geometric variations in dynamical systems. The addition of studies of chaotic systems from the geometric perspective, as we have done, provides the opportunity to establish criteria for choosing one chaotic system over another when the chaotic behavior is constant.
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