Degree heterogeneity shapes escape mechanisms in networks of diffusively coupled bistable elements

TL;DR

This paper explores how degree heterogeneity influences escape mechanisms in networks of diffusively coupled bistable elements, extending previous fully connected models and providing analytical tools for understanding complex state transitions.

Contribution

It generalizes the escape mechanism classification to heterogeneous networks using an analytical framework based on the annealed network approximation.

Findings

Degree heterogeneity affects escape mechanisms alongside coupling strength.

Validated theoretical predictions with numerical simulations.

Provided effective one-dimensional descriptions of collective escape dynamics.

Abstract

For fully connected populations of diffusively coupled bistable elements, we identified three qualitatively distinct mechanisms of noise-induced escape as coupling strength varies [H. Ishii and H. Kori, arXiv:2512.01388 (2025)]. Here we generalize these results to a class of networked systems and demonstrate that degree heterogeneity (i.e., variability in node degree) shapes escape mechanisms alongside coupling strength. In applied contexts, networks of noisy bistable elements provide a minimal conceptual framework for understanding abrupt state transitions in complex systems. Theoretically, a quantitative approach to escape is challenging because nonlinearity, network interactions, and dynamical noise jointly shape the collective dynamics. We extend the analytical framework developed for the fully connected model to a class of networked systems based on the annealed network approximation. We derive three effective one-dimensional descriptions of collective escape dynamics. We validate our theoretical predictions for mean escape times by direct numerical simulations. Our analysis reveals that the validity and quantitative behavior of the reduced descriptions depend on degree heterogeneity in addition to coupling strength. This work extends the classification of escape mechanisms to networked bistable elements. Furthermore, our analytical framework provides tools for understanding synergistic phenomena arising from the interplay of nonlinearity, diffusive coupling, and dynamical noise.