I have always found that tabulating information, cases and sub-cases, is very useful in providing a coherent picture of the situation, making interlinks visible, as well as general rules.

In the context of **Dynamic Economics**, stability of differential equations that describe laws of motion of economic variables are of primary interest. Since in Economics we are almost exclusively concerned with the existence of “**saddle-path stability**“, we usually do not provide the whole picture and possibilities, of which saddle path stability is just one case.

So **I wrote and I attach here a summary of what can happen (and when) in a 2 by 2 system of differential equations, in terms of the system’s stability.** While writing it, I hit upon an interesting way to show how important is the actual arrangement of equations when one wants to use matrix algebra -arrangements that are equivalent in the “plain” formulation of a system of equations, become totally different if viewed through the lenses of matrix algebra, and lead to different results.

The summary can be downloaded here:

Stability of Systems of Diferrential Equations

Maybe in the future I will do the same for Difference Equations, since they are more convenient when one wants to work in a stochastic framework.