Internal reliability and antireliability in dynamical networks
Tommaso Matteuzzi1, Franco Bagnoli1,2, Michele Baia1,2
1University of Firenze, Department of Physics and Astronomy and CSDC, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy.
Physical Review. E
|November 18, 2025
Summary
We introduce internal reliability for dynamical networks, assessing unit synchronization. Peripheral units are often antireliable, while central units tend to be reliable, depending on coupling.
Area of Science:
- Dynamical systems and network theory
- Statistical physics
- Computational neuroscience
Background:
- Understanding the stability and behavior of interconnected units is crucial in complex systems.
- Internal reliability defines how well replicated units in a network maintain their intended states.
Purpose of the Study:
- To define and quantify internal reliability in finite dynamical networks.
- To analyze reliability patterns in various coupled oscillator models, including the Kuramoto model.
- To investigate the impact of coupling (attractive vs. repulsive) on unit reliability.
Main Methods:
- Definition of internal reliability based on state synchronization with prototypes.
- Quantification using the transversal Lyapunov exponent.
- Analysis of the Kuramoto model with distributed natural frequencies.
- Examination of other coupled oscillator models (Winfree, rotators, Stuart-Landau).
Main Results:
- Peripheral units are antireliable and central units reliable under attractive coupling before synchronization.
- Repulsive coupling reverses this pattern: central units are antireliable, peripheral ones reliable.
- Large subnetworks and recurrent neural networks exhibit antireliability, while individual units are reliable.
- Reliability in the Kuramoto model relates to phase correlations via a fluctuation-dissipation-like relation.
Conclusions:
- Internal reliability is a quantifiable property of dynamical networks, influenced by unit properties and network topology.
- The study reveals distinct reliability patterns in coupled oscillator systems, offering insights into network stability.
- Findings are consistent across multiple coupled oscillator models, suggesting generalizable principles.
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