Bounds of Validity for Bifurcations of Equilibria in a Class of Networked Dynamical SystemsPranav Gupta, Ravi Banavar, Anastasia Bizyaevahttps://arxiv.org/abs/2510.10215 https…
Bounds of Validity for Bifurcations of Equilibria in a Class of Networked Dynamical SystemsLocal bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of validity for the classification of bifurcation diagrams in two classes of continuous-time networked dynamical systems, analogous in structure to the Hopfield and the Firing Rate dynamic neural network models. Our approach leverages recent advances in computi…