  Bifurcation phenomena are common in multi-dimensional multi-parameter
dynamical systems. Normal form theory suggests that the bifurcations themselves
are driven by relatively few parameters; however, these are often nonlinear
combinations of the bare parameters in which the equations are expressed.
Discovering reparameterizations to transform such complex original equations
into normal-form is often very difficult, and the reparameterization may not
even exist in a closed-form. Recent advancements have tied both information
geometry and bifurcations to the Renormalization Group. Here, we show that
sloppy model analysis (a method of information geometry) can be used directly
on bifurcations of increasing time scales to rapidly characterize the system's
topological inhomogeneities, whether the system is in normal form or not. We
anticipate that this novel analytical method, which we call time-widening
information geometry (TWIG), will be useful in applied network analysis.
