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The straightforward approach
I adopted the approach suggested in an earlier post (http://www.mapleprimes.com
/questions/137320-Plotting-A-System-Of-Ode) for the known results,
but some part of curve is missing.
The output I got is

and the known results are

I increased the Digit, numpoints and also went for high grid size but no luck.
I thought maybe some one would like to have a look and will help me out.
Thanks
paraplot.mw