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| This image created with the basin of attraction algorithm is based on the dynamical system characterized by the expression x''=a*cos(t)-x*x*x-μ*x'. This system has 5 attractors. The one whose basin of attraction wraps all around the outside of this image is the most powerful on the basis of the amount of the map of all possible states that it owns , but not very interesting. This image highlights the next two most powerful attractors, one in gold and one in blue, each featured separately in the previous two images. Since they are nearly equally powerful attractors, their basins of attraction are quite thououghly intermingled. The domain of the map of possible states for this system covered by this image is: (-1, 0.387)/(0.5, -0.7) The parameter values are a=0.2, μ=0.08. |