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I'm writing a piece in which at some point there is a shift to a new subject called stochastic dynamical systems. The transition looks like follows

...but once dynamical noise is introduced the relevant mathematical framework becomes stochastic dynamical systems.

But this doesn't sound quite right to me. I've considered the following alternative

...but once dynamical noise is introduced the relevant mathematical framework becomes that of stochastic dynamical systems.

Is there a better way of phrasing this?

If there are more appropriate tags for this question please feel free to add them.

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    Does the sentence mean "When xyz is introduced , we have to apply a new framework to the problem" , or "When xyz is introduced , the framework transforms into something else?" (Latter does not seem a plausible option, but even then it's better to know)
    – R.S.
    Commented Oct 11, 2020 at 13:03
  • @R.S. The former.
    – H.Rappeport
    Commented Oct 11, 2020 at 13:07
  • Yes, the mismatch of number is jarring, and adding padding (I wish I hadn'r said that) makes things less incongruous. Distance lends enchantment to the view. Another solution: 'but once dynamical noise is introduced the relevant mathematical framework becomes the stochastic dynamical systems model.
    – Edwin Ashworth
    Commented Oct 11, 2020 at 13:09
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    stochastic dynamic systems
    – Xanne
    Commented Oct 12, 2020 at 6:26
  • @Xanne Yes, I thought that too, but google steamrolled the puritan in me with over a million results.
    – R.S.
    Commented Oct 12, 2020 at 10:55

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I would insert a short reason for the transition before mentioning the new framework. Something like -

...but once dynamical noise is introduced the added randomness (or whatever) takes the process/problem into the realm of another framework, called stochastic dynamical systems.

If the reader is already familiar with the new framework then we can drop 'another framework` bit and the flow of sentence becomes even smoother.

...but once dynamical noise is introduced the added randomness (or whatever) takes the process/problem into the realm/domain of stochastic dynamical systems.

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