Lyapunov Exponents of a Forced Logistic map
See the September 1991 issue of Scientific American
The Fractal Rabbit Lyapunov Wing of the Savage Rabbit Art Gallery proudly presents these creations by Savage Rabbit Artists and SCO employees Ronald Joe Record and Andrew Sharpe. These fantastic creations represents the Lyapunov exponents of a forced oscillator modelled by parameterizing the logistic map. The Lyapunov exponent(s) of a dynamical system can be used to numerically characterize the qualitative behaviour of the system. A positive Lyapunov exponent is indicative of rapidly diverging orbits or "sensitive dependence on initial conditions". This is one characteristic of "chaos".
Colors represent the behaviour of the model ranging from stable periodic or fixed orbits to chaotic or "strange" attractors. The color figure graphically divides parameter space into stable and chaotic regions.
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