# Plotting basin boundary [duplicate]

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.

## marked as duplicate by user9660, MarcoB, m_goldberg, Yves Klett, J. M. will be back soon♦Jul 7 '16 at 0:33

• I suggest you read the documentation of DSolve and NDSolve. – shrx Nov 22 '13 at 13:52
• @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