Plotting basin boundary

Question

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.

I suggest you read the documentation of DSolve and NDSolve. — shrx, Nov 22 '13 at 13:52
@shrx really? where does it discuss basin boundaries in the docs? — rcollyer, Nov 22 '13 at 13:56
@rcollyer I thought he needed to solve those equations first, because he did not provide any code except the equations themselves. — shrx, Nov 22 '13 at 13:58
@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. — rcollyer, Nov 22 '13 at 13:59
@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. — rcollyer, Nov 22 '13 at 14:13
I am sorry. I have not give a clear describe. This issue was come from:link — HQH, Nov 23 '13 at 06:20

Plotting basin boundary

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