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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. Two of them are simple closed loops in state space, representing an oscillation of the system's moving part with a period equal to that of the driving force. One attractor is a twisted three-part loop resulting in much more complicated motion of the system. The remaining two are a symmetrical pair of two loop attractors. The region of the domain colored in gold contains the set of initial conditions that lead to one of this pair of attractors. |