An extreme dimensional reduction emerging from systems of polynomial differential equations

What is it about?

The paper explains how to apply a particular variable change on systems of first-order polynomial ordinary differential equations. Looking at some properties of the new dynamic variables, it is possible to identify an attractive region where the evolution could be described with a single equation, no matters how complicated the original systems is.

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Why is it important?

This is the first paper that studies the application of this variables transformation to chemical kinetics. Since this mathematical architecture underlies the description of any reactions scheme (and other interesting physical systems as well), this study could be very important for studying the long-time behavior of many systems.