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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, (-1.285, 0.9722)/(1.285, -2.282). 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. |