How to show that 2 DVs follow different nonlinear trends along one IV

I have collected data on an experiment where I measure two dependent variables: detection of a stimulus, and accuracy making a judgement on that stimulus. There is one independent variable, with 11 levels. This is what the data looks like:

The black line represents proportion of detected trials, and the red line represents proportion of correct trials.
I would like to show that detection (black) and discrimination (red) do not follow the same trend. Ideally I would demonstrate that at SOA=7 they do start following the same trend, and thus that there's a dissociation in their trends along the levels of SOA.
Could anybody recommend a way in which I could prove that?
Detection fits with a quadratic model, and discrimination does not, but that is not proof enough.
Any clues would be extremely helpful!
Thank you very much!!! ;););););););)