Quantify limits of dimensionality reduction with coupled long-time degrees of freedom

Ascertain the conditions and extent to which the effective one-dimensional reduction remains valid for chemical reaction networks when more than one degree of freedom is effectively operative in the long-time dynamics; determine how far dimensionality can be reduced without compromising fidelity when degrees of freedom are coupled.

Background

The proposed reduction scheme is most accurate when a single degree of freedom effectively governs the long-time behavior, achieved by freezing other compartments on the mean-field manifold. In systems where multiple degrees of freedom are coupled and remain active asymptotically, the applicability and accuracy of the one-dimensional reduction are uncertain.

The authors explicitly note that the extent of permissible reduction in such coupled scenarios is not yet clear, highlighting the need to characterize when and how multi-degree dynamics can be faithfully captured by a reduced model.