Below are the windowed Fourier ridges of the sum of parallel linear chirps.
The two frequencies are well detected.
Now the ridges of a sum of chirps:
Between t=500 and t=600, the transform fails to discriminate the frequencies because of its limited frequency resolution.
The limited time resolution at high frequencies explains why the windowed Fourier transforms fails to track the instantaneous frequencies of the sum of two hyperbolic chirps:
Indeed, the instantaneous frequencies vary too much within the Fourier window when close to the asymptote.
Conclusion on Instantaneous Frequency Detection