Dresden 2026 – wissenschaftliches Programm

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 16: Tipping Points in Social and Climate Systems (accompanying session for SYTP)

SOE 16.4: Vortrag

Donnerstag, 12. März 2026, 12:30–12:45, GÖR/0226

Jacobian Reconstruction from Time-Series of an Opinion Dynamical Network Model and its Applicability as an Early Warning Signal for Tipping Points — •Tim Mauch — Helmholtz Institute for Functional Marine Biodiversity (HIFMB), Im Technologiepark 5, 26129 Oldenburg, Germany — Carl-von-Ossietzky University, Institute for Chemistry and Biology of the Marine Environment, Carl-von-Ossietzky Str. 9-11, 26129 Oldenburg, Germany

In social dynamical systems the early identification of critical transitions is a significant challenge. To address this, we formulate a new opinion model to enhance the understanding of tipping mechanisms in opinion dynamics and adopt a method for reconstructing the Jacobian matrix of the model from time-series data, testing its applicability for detecting critical transitions.

Inspired by meta community models from ecology, we study opinion formation using a network-based model in which nodes represent communities of interacting agents holding one of two competing opinions, and links represent avenues of migration. We analytically derive conditions for diffusion-driven pattern formation and identify a mechanism facilitating opinion diversity, where the minority opinion can reach local majority, thus creating regions of differing opinion dominance.

We then generate synthetic time series of the model and reconstruct the Jacobian matrix using only the time series data and the underlying network structure. We show that the reconstructed eigenvalues correctly capture the trend of the analytical eigenvalues when changing the model parameters towards critical transitions.

Keywords: Tipping Points; Opinion Dynamics; Jacobian Reconstruction; Networks