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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(ω*t+φ)-b*(x-x3)-μ*x',
where x' is the first derivative of x with respect to time, t, and x'' is the second derivitave of x with respect to time.
The domain of the map of possible states for this system covered by this image is, (-10, 15)/(10, -15). The parameter values are a=5, ω=1, φ=0, b=-1 and μ=0.25. This system has two attractors, one of which is so convoluted that the imaging algorithm gives up and splits it into two parts each with its own basin of attraction (blue and yellow). See the Twisted Core image for the result of increasing the friction coefficient from 0.25 to 0.315 to tame the wild attractor. |