Resolution:
## Figure 3.
The asymptotically stable equilibrium point. The stable equilibrium (X) is illustrated by trajectories and phase orbits in the 18D space with 10% perturbations.
The red line: the original curve with respect to the experimental initial value [5]; the yellow/blue lines: the curves whose initial value has a -10%/+10% perturbation
from the experimental one; the triangular spots: projections of _{eq}Xon the corresponding dimensions. (A) Asymptotical stability shown by trajectories.
Each subplot represents a dimension in the 18D space, i.e. the kinetics of a metabolite.
All trajectories eventually and consistently converge to the _{eq }X(projection on the corresponding dimension) although a 10% perturbation is in the
initial value. The x-axis: time (s); y-axis: concentration (mM). (B) Asymptotical
stability shown by phase orbits. Stability is more clearly illustrated in such presentation.
We randomly chose 2 state variables (metabolites #7 and #8 in the plot) to form the
phase orbit in the 2D subspace. Arrows denote the directions of orbits and they eventually
and consistently converge to _{eq }X(projection on the 2D subspace, marked by the triangular spot). For other 2D subspaces,
the orbit profiles are the same.
_{eq }Li and Liu |