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I am looking at the system:

$2X + Y \Leftrightarrow 3X $

$A \rightarrow Y$

$X \rightarrow B$

The description in terms of differential equations is this:

$\frac{dx}{dt} = x^{2}y - x$

$\frac{dy}{dt} = a - x^{2}y$

What is puzzling me is that the fact that 3X are produced is not captured in these equations.

Why is the description not something like

$\frac{dx}{dt} = 3x^{2}y - x - x^{3}$ ?

What fundamental thing am I missing? Help is greatly appreciated.

(also, I have a hard time finding relevant tags for this, so please feel free to change)

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  • $\begingroup$ Not my area and, checking the basics, such as here and here, I also can't say why - and also don't get why the coefficient b can be omitted. Have you tried asking at Chemistry SE? BTW, it'd be good to name your source for these equations. $\endgroup$
    – stafusa
    Commented Feb 8, 2021 at 19:10
  • $\begingroup$ Thanks, for your reply. B can be omitted because the reaction from X to B is unidirectional, so B has no influence on X. I haven't asked at chemistry SE, but this is a good idea. The book this is from is "Mathematical models in biology" by Leah Edelstein-Keshet $\endgroup$
    – warped
    Commented Feb 8, 2021 at 21:58

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