During the mathematical process and specifically through the model execution, one found the results are oscillated, one time converge and another time diverge. Sometime converge in place and diverge in other.
Mathematically speaking, your question is "ill-posed". For as long as you ask it in such general form, there are too many possible answers. The reasons could be the resonance in response to external perturbation, bifurcations in the model, synchronization, sensitivity to data leading to unpredictable (chaotic) behavior, or computational errors, to mention a few.
The most associated divergence problems with the mathematical modeling are assessed inside the model domain representing in the initial and boundary conditions. There is no generalization in the Q as claimed.