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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)-x3-μ*x',
where x' is the first derivative of x with respect to time, t, and x'' is the second time derivative of x.
The domain of this image in the map of possible states for this system is, (-3.102, 9.81)/(4.988, -9.91). The parameter values are a=21.45, ω=1 φ=0, b=1, and μ=0.025. There is a single attractor for this system but it is so extensive that we can fool the basins of attraction algorithm into reading separate parts of it as individual attractors. Color Bird is an extreme example of this imaging technique. |