Sloppy model analysis identifies bifurcation parameters without Normal Form analysis

TL;DR

This paper introduces a novel method called time-widening information geometry (TWIG) that uses sloppy model analysis to identify bifurcation parameters in complex dynamical systems without requiring normal form transformations.

Contribution

The paper presents TWIG, a new analytical approach leveraging information geometry to analyze bifurcations directly, bypassing the need for difficult normal form reparameterizations.

Findings

TWIG effectively characterizes topological inhomogeneities in dynamical systems.

The method works on systems with increasing time scales, regardless of normal form existence.

TWIG offers a rapid alternative to traditional bifurcation analysis methods.

Abstract

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.