Question: Graphing parameter domain for a coupled ode system

Hello everyone,

I saw a question on a different forum related to the stability of the numerical solution of a coupled ode system. The original question was about the convergence of the far field condition (infinity) for some specific values of the different parameters involved.  For the details please see the link below

http://mathematica.stackexchange.com/questions/33538/numerical-solution-of-coupled-odes-with-boundary-conditions

But I was/am wondering, whether is it possible to graphically show that some specific parameters has a specific domain for which all the boundary conditions are satisfied? This will help to choose appropriate values for the parameters involved and therefore, will have no convergence issue.

The questioner coupled system was 

and he/she was facing problem with the convergence of the far field boundary condition for zeta =3, n=1 and zeta=1, n=5 using Mathematica. But with maple, there is no such issue, I have tried the above mentioned values and the solution satisfies the bcs.  

So, what I am trying to find out here is that before we go for the solution for some specific values of the different parameters, I want to find a way to graph the domain of those parameters for stable solution and later on use the values in the specific domain for further analysis.

For convenience, I have uploaded the maple sheet. The name of the file is misleading somehow but I have just type the equations nothing else if someone want to try?

Paraplot.mw

Thanks