Both MatLab and mathematica can do it.
http://www.mathworks.com/matlabcentral/fileexchange/16731-forced-duffing-oscillator
http://demonstrations.wolfram.com/DuffingOscillator/
http://tinyurl.com/gmqnywl
In the following link http://yorke.umd.edu/dynamics/ you can download the software DYNAMICS written by Prof. James A Yorke. The program contains a subroutine by which you can directly plot basins of attraction by simply applying a command BAS. You might need to install it and "play" a bit with the software to gain a feeling of the different basins you can obtain. You might need to read the manual to understand a bit how to use the commands. Of course, you can also use any of the the languages suggested by the above colleagues to compute them as well.
@ Miguel A F Sanjuan:
Respected sir,
Thanks a lot for the useful link.
Chandan
@ Chandan Bose,
In a Duffing Oscillator, you can have co-existing chaotic and periodic solutions. A transfer map that relates the system states that are one time period apart can be used to distinguish the periodic solutions from the chaotic ones. To plot the basins of attraction,
1) Divide the phase space into finely divided very small regions.
2) From each region pick a point and subject it to the transfer map above for a sufficient number of iterations.
3) By doing this, the periodic behavior can be identified if the sequence of states repeat.
4) Such initial conditions correspond to a periodic attractor.
5) The initial conditions for which the states do not repeat after a sufficiently high number of iterations correspond to the chaotic attractor.
6) Appropriately color code these initial conditions to obtain the basins of attraction.
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