Stability of Systems of Differential Equations

Posted: April 13, 2014 in Educational Material
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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.

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