Taffy

Explanation of the Image...

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)-x ^{3}-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, 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. |