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This question already has an answer here:

How to plot the basin boundary in Mathematica?
I have been trying to do this using the system

y''[t] == -R y'[t] + (( Y[1] - y[t])/(Sqrt[(X[1] - x[t])^2 + (Y[1] - y[t])^2 + d^2])^3 
                     + (Y[2] - y[t])/(Sqrt[(X[2] - x[t])^2 + (Y[2] - y[t])^2 + d^2])^3 
                     + (Y[3] - y[t])/(Sqrt[(X[3] - x[t])^2 + (Y[3] - y[t])^2 + d^2])^3) 
          - c y[t]

x''[t] == -R x'[t] + ((X[1] - x[t])/(Sqrt[(X[1] - x[t])^2 + (Y[1] - y[t])^2 + d^2])^3 
                     + (X[2] - x[t])/(Sqrt[(X[2] - x[t])^2 + (Y[2] - y[t])^2 + d^2])^3 
                     + (X[3] - x[t])/(Sqrt[(X[3] - x[t])^2 + (Y[3] - y[t])^2 + d^2])^3) 
          - c x[t]

It is a magnetic pendulum swinging chaotically about 3 other magnets underneath. R,c,d are all constants,where r is air resistance, d is the vertical distance of the pendulum from the floor, c is the sping constant of the pendulum. X[1], X[2] and X[3] (Y[1],Y[2] and Y[3]) are the coordinates of the magnets.

But I have gotten nowhere.

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marked as duplicate by user9660, MarcoB, m_goldberg, Yves Klett, J. M. is away Jul 7 '16 at 0:33

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  • $\begingroup$ I suggest you read the documentation of DSolve and NDSolve. $\endgroup$ – shrx Nov 22 '13 at 13:52
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    $\begingroup$ @shrx really? where does it discuss basin boundaries in the docs? $\endgroup$ – rcollyer Nov 22 '13 at 13:56
  • $\begingroup$ @rcollyer I thought he needed to solve those equations first, because he did not provide any code except the equations themselves. $\endgroup$ – shrx Nov 22 '13 at 13:58
  • $\begingroup$ @shrx he needs to provide X, Y, R, c, and d and boundary conditions, but otherwise that is code that would be supplied to the solvers. $\endgroup$ – rcollyer Nov 22 '13 at 13:59
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    $\begingroup$ @HQH which basins are you looking for? The basins of attraction for each magnet, or the chaotic basins? They're subtly different. The first is much, much simpler. $\endgroup$ – rcollyer Nov 22 '13 at 14:13