Investigate application of ODEs

[cxd]

after spending this last semester learning about dynamical systems, phase plots, application of ODEs to qualitative analysis of phases of dynamic systems. Explore application of ODEs in the domain of statistical learning. Are ODEs simply applied in optimisation processes only?
Is there an manner in which the qualitative analysis used in dynamical systems able to be applied in the domain of statistical models, such as in time series analysis?

Alternately, there is definitely the ability to apply modelling in terms of control algorithms, perhaps explore that further in relation to playing with sphero for navigation and control.

Is there also an application of dynamical modelling in image processing? For example models of light and colour? Do some investigation into this also.