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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*x3-μ*x',
where x' is the first derivative of x with respect to time, t, and x'' is the second derivative of x with respect to time.
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, ω=1, φ=0, b=1 and μ=0.08. This system has five attractors, one of which attracts the system when the initial conditions lie in the blue colored area of the domain. As you can see, without this basin of attraction map it would be difficult to predict what behavior the system would settle on for any given initial conditions. |