LYAPUNOV PLAY

Mario Markus of Max Planck Institute for Nutrition has used dynamical systems to study the evolution of animal populations- --the change over time of food, fertility, size, etc.-- with dynamics requiring the ability of reproduction to alternate quasi-periodically between two values. Such systems can show both a stable cycle and chaotic evolution depending on the fertility ability. Stability or chaos can be analysed by computing the so-called Lyapunov exponent. (Lyapunov was a Russian mathematician living at the end of the 19th century). Markus-Lyapunov images are colour mappings of the Lyapunov exponent versus fertility, along horizontal and vertical axes. Only the stability domain is plotted; here, chaos (i.e. positive Lyapunov exponent) is rendered in dark blue. As the exponent goes from 0 to minus infinity, shades range from light to dark. At zero, the chaos threshold, tlighter shade. There is clearly much that is arbitrary in this colour mapping, and this gives an opportunity for choices based on aesthetic considerations. The picture consists of seven original Markus-Lyapunov pictures which were superimposed and reworked.