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. 2023 Oct 25;20(207):20230505. doi: 10.1098/rsif.2023.0505

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Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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Figure 7. — Graphical description of the dynamic decomposition theorem (applied to example A.9). The dynamics of $F_{1} ⋊_{P} F_{2}$ can be seen as a semi-direct product between the dynamics of F₁ and the dynamics of F₂ induced by F₁ via the coupling scheme P. The dynamics of F₂ induced by attractors of F₁ can vary, and the dynamic decomposition theorem (theorem A.7) shows precisely how to combine all of these attractors.