Phase Diagram - growth model The dynamics of Ramsey-Cass-Koopman growth model is usually summarized in phase diagrams with the 2 equations (conventional symbols apply):
\begin{align*}
\frac{\dot c}{c}=&amp;\frac{r-\rho}{\theta}\\
\\
\dot k =&amp; f(k) - (n+g+\delta)k
\end{align*}

From these equations you work out the equilibrium and whether it is a saddle path. 

However this analysis is static; some of those parameters are time varying (e.g., 1950 population growth isn't the same as in 2017). How can you represent these changes in this essentially static graphical framework?
In control systems engineering, there was the "Aizerman Conjecture" (the transliteration of Aizerman varies) that argued that a linear time-varying system was stable if the parameters (state matrices) at all times corresponded to stable systems. However, counter-examples were found to this conjecture.

About the only way to show that a time-varying system is stable (for example) is to find a Lyapunov function that holds at all times. This is generally going to be difficult.

Something like graphical analysis would be technically invalid, as you are violating assumptions that are in place. You are pretty much going to have to derive any results from first principles.