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Sloppy model analysis identifies bifurcation parameters without normal form analysis.

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Summary
This summary is machine-generated.

This study introduces time-widening information geometry (TWIG) to identify key parameters controlling bifurcations in complex dynamical systems. TWIG simplifies analysis by revealing parameters that define system topology, regardless of normal form.

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Area of Science:

  • Dynamical Systems Theory
  • Information Geometry
  • Network Analysis

Background:

  • Bifurcations in complex systems are often driven by nonlinear parameter combinations, making analysis difficult.
  • Traditional methods struggle to find reparameterizations for complex models to reach normal form.

Purpose of the Study:

  • To develop a novel analytical method for identifying parameters controlling bifurcations in multidimensional multiparameter dynamical systems.
  • To overcome limitations of normal form theory in analyzing complex models.

Main Methods:

  • Utilizing information geometry and sloppy model analysis with the Fisher information matrix.
  • Analyzing observations over extended timescales to identify parameters characterizing topological inhomogeneities.

Main Results:

  • Demonstrated that information geometry can identify bifurcation-controlling parameter combinations.
  • Developed a new method, time-widening information geometry (TWIG), applicable even when systems are not in normal form.
  • Identified parameters that rapidly characterize system topological inhomogeneities.

Conclusions:

  • TWIG offers a powerful approach to analyze bifurcations in complex dynamical systems.
  • The method is robust, working for systems not conforming to normal form.
  • TWIG is expected to be valuable for applied network analysis.