Question: How to convince dsolve, numeric I'm working with a real ODE system

I have this very ugly ODE system which I solve with "dsolve, numeric, complex=true". It works ok but I'd really like to be able to use events. The problem is that the solution of the system has very small (~10^(-Digits)) imaginary part and as we know "events" works only for real ODEs.

My question is does anyone know a way to force dsolve to solve the ODE as a real system? In Mathematica, there is the function "chop" which does the trick. In Maple, I tried with fnormal and also by forcing some terms to be real but that makes it hit a singularity at 0.01 which doesn't exist when it integrates it as a complex system. In Mathematica, it integrates ok with "chop" without any random singularities. 

I'm currently trying separating the system into real and imaginary parts, but considering how ugly the system is, it may not be so simple (and so far, it doesn't work). So something to trick dsolve would come handy.

Thanks in advance.

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